[Wolfram's cosmological principle and Viktor Toth's criticism of f(div) theory] - A New Kind of Science: The NKS Forum

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# Wolfram's cosmological principle and Viktor Toth's criticism of f(div) theory

Posted by: David Brown

According to NKS, there is a finite, digital model that unifies quantum field theory and general relativity theory. Consider Wolfram’s cosmological principle:
THE MAXIMUM PHYSICAL WAVELENGTH EQUALS THE PLANCK LENGTH TIMES THE FREDKIN-WOLFRAM CONSTANT.
Can quantum field theory explain the vacuum energy?
http://en.wikipedia.org/wiki/Vacuum_energy
By assuming that M-theory combined with Wolfram’s cosmological principle explains both dark matter and dark energy, the f(div) theory of modified general relativity and also the existence of paradigm-breaking photons become plausible.
From http://en.wikipedia.org/wiki/Virtual_particle
“A virtual particle is one that does not precisely obey the m^2c^4 = E^2 - p^2c^2 relationship for a short time. In other words, their kinetic energy may not have the usual relationship to velocity — indeed, it can be negative. The probability amplitude for them to exist tends to be canceled out by destructive interference over longer distances and times. They can be considered a manifestation of quantum tunnelling. The range of forces carried by virtual particles is limited by the uncertainty principle, which regards energy and time as conjugate variables; thus virtual particles of larger mass have more limited range.
There is not a definite line differentiating virtual particles from real particles — the equations of physics just describe particles (which includes both equally). The amplitude that a virtual particle exists interferes with the amplitude for its non-existence; whereas for a real particle the cases of existence and non-existence cease to be coherent with each other and do not interfere any more. In the quantum field theory view, "real particles" are viewed as being detectable excitations of underlying quantum fields. As such, virtual particles are also excitations of the underlying fields, but are detectable only as forces but not particles. They are "temporary" in the sense that they appear in calculations, but are not detected as single particles. Thus, in mathematical terms, they never appear as indices to the scattering matrix, which is to say, they never appear as the observable inputs and outputs of the physical process being modelled. In this sense, virtual particles are an artifact of perturbation theory, and do not appear in a non-perturbative treatment.”

In the f(div) theory of M-theory with alternate universes, there are several paradigm shifts:
(1) The Fredkin-Wolfram information process is the proto-physical reality underlying the unique, physically valid computational method for M-theory. This bizarre information process makes use of informational substrate to "compute" Nambu digital data by means of the Fredkin delivery machine. The bizarre information process then makes use of Nambu digital data to "compute" digital physical reality by means of the Nambu transfer machine. The Fredkin-Wolfram information process is spread across huge multitudes of alternate universes.
(2) There are a huge, but finite, number of alternate universes.
(3) There is an informational substrate below the Planck scale — this substrate is governed by a hidden determinism that establishes the fundamental law of the multiverse: Informational substrate makes Nambu digital data makes digital physical reality. The 11-dimensional supersymmetric model governs the smoothing of Nambu digital data with respect to Nambu spacetime and Nambu energy.
(4) Nature is finite and digital with virtual mass-energy in 4 basic categories from the viewpoint of an observer in a particular observable universe belonging to the multiverse. The four categories are:
(a) virtual mass-energy explicitly observed and made real by Fredkin-Wolfram computation for the observable universe in the sense of satisfying the equivalence principle;
(b) virtual mass-energy implicitly observed and made real by Fredkin-Wolfram computation for the observable universe in the sense of satisfying the equivalence principle;
(c) virtual mass-energy made partially real and partially non-real by Fredkin-Wolfram computation for the multiverse in the sense of having non-zero gravitational mass-energy and zero inertial mass-energy;
(d) virtual mass-energy made observationally irrelevant by Fredkin-Wolfram computation for the multiverse in the sense of having no effect whatsoever on the observational universe.
(5) Quantum field theory and general relativity theory make incorrect predictions because those two theories ignore Wolfram’s cosmological principle.

What might be an excellent criticism of the f(div) theory? Viktor T. Toth has provided such a criticism in answer to the question as to whether f(div) theory and M-theory with alternate universes can explain the Pioneer anomalous acceleration:
“I don't think I'm the right person to answer your question, as I am not a fan of string theory/M-theory, and I haven't read Wolfram's book, so any opinion I might have about it is second-hand.

Although I have no idea what "f(div) theory" is, and a quick Google search did not leave me particularly enlightened, I have considered many possible causes of the Pioneer acceleration. However, before we can establish if it truly exists, I think such speculations are premature. At the time of the announcement of the anomaly, no proper analysis of the craft's thermal behavior was done, and the analyses that have since been performed all suggest that thermal radiation is the likely culprit. A more sophisticated thermal model is in the works, which can hopefully settle this question with some degree of certainty in the near future.

Your proposed modification of Einstein's field equation may not be derivable from a Lagrangian theory. Most physicists would consider that a huge drawback. On the other hand, if it turns out that you can derive the proposed equation from a Lagrangian action, it means that the solution would satisfy conservation laws of some form. In any case, I don't see how the proposed modification would change the (weak) equivalence principle, as the stress-energy tensor on the right-hand side is still independent of the constitution of matter, and the amount by which matter affects geometry and is affected by it (i.e., the equivalence of active and passive gravitational mass) remains the same. I'd also worry about running into observational constraints (precision solar system observations, Eötvös-type laboratory experiments.)

What you call "virtual mass-energy" does have inertial mass. This is definitely supported by experiment. For instance, the difference in mass between a helium atom and a deuterium molecule (same particle content) comes from the binding energy (i.e., virtual photons) in the helium atom. Eötvös-type experiments have demonstrated clearly that such binding energies contribute to both gravitational and inertial mass.”

Toth correctly point out 2 key issues.
(1) The f(div) theory is definitely not derivable from a Lagrangian theory. Unless M-theory and the Fredkin finite nature hypothesis are both true, then f(div) theory is false.
(2) Is binding energy = mass-energy of virtual photons? Toth and almost all other physicists say yes, but I say no — or, more precisely, binding energy = mass-energy of those virtual photons that are either explicitly or implicitly observed. Explicit or implicit observation makes virtual mass-energy into 100% real mass-energy. In the f(div) theory of dark matter, binding energy = mass-energy of Fredkin-Wolfram observably-computed virtual photons, but dark matter has mass-energy = mass-energy of Fredkin-Wolfram non-observably-computed virtual photons; the non-observably-computed virtual photons possess non-zero gravitational energy but zero inertial mass-energy. The Fredkin-Wolfram information process computes virtual photons that manifest themselves in our universe and satisfy the equivalence principle. The Fredkin-Wolfram information process also computes virtual photons that partially manifest themselves in our universe and partially manifest themselves in alternate universes and possess non-zero gravitational mass-energy and zero inertial mass energy. The second type of Fredkin-Wolfram computation explains dark matter.
In reply to my point, “Is binding energy = mass-energy of virtual photons? You say yes, but I say no” — Toth replied, ”I don't think this is a matter of personal opinion. In the context of quantum field theory (which is the context in which terms like "binding energy" and "virtual photon" are defined), the binding energy inside an atom is due to the exchange of virtual photons. These energies are measurable, are accurately predicted by theory, and they accurately obey the equivalence principle, as demonstrated by Eötvös-type experiments.”

D.B. email to V. Toth: “According to you, the properties of virtual photons are not a matter of personal opinion. I disagree for at least 2 reasons: First, I think the mathematical foundations of quantum field theory are logically unsatisfactory. Second, I think that quantum field theoretic perturbative calculation excludes those virtual photons that are partially in our observable universe and partially in alternate universes.”

Viktor Toth: “My understanding of virtual particles does not come from Wikipedia, but from quantum field theory textbooks. While it is true that a virtual particle can be "off shell", that is not its most important characteristic. What a "virtual particle" really is is a higher-order term in a series expansion of a path integral. These higher order terms are known to high precision to have both gravitational and inertial mass, i.e., the contribution to the overall mass of a compound particle that arises from internally exchanged virtual particles is known to satisfy Eötvös-type experiments. The range of a force depends on the rest mass of the particle carrying that force. Thus, electromagnetism with its massless photon has infinite range: the needle of a compass, for instance, exchanges virtual photons with the loop currents in the Earth's interior thousands of kilometers away as it responds to what we perceive as the magnetic force. This is true despite the fact that the virtual photons thus exchanged may be off-shell with nonzero rest mass. There is a definite line between virtual particles and real particles: in a quantum field theory calculation, real particles correspond to the external lines of a Feynman diagram, whereas virtual particles are the internal lines. In any specific calculation, the external lines correspond to particles that are observed, whereas the internal lines represent the various processes that can connect the observed particle content. As to QFT being "unsatisfactory", with M-theory, alternate universes, or a digital universe being offered as more satisfactory alternatives, all I can say is that QFT predicts tangible things that are spectacularly confirmed by experiment. The theory may be ugly, but it works, it has genuine predictive power, and it is falsifiable.”
http://www.vttoth.com

Posted by: mdmd

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