Backreaction: Consciousness and Physics from Scratch
backreaction.blogspot.com/.../consciousness-and-physics-from-scratch.ht...
May 5, 2014 - Titled “Consciousness as a state of matter”, the paper scores at 30 pages in 10 pt font. ... These subsystems are not local in any way, they are generic ... Tegmark only acts with these transformation on the density matrix, so I am not sure ...... but not zero state the XY Lorentz symmetry does not hold in general
Max Tegmark: "In Section III, we discussed the challenge of deriving our perceived everyday view (the "frog's view") of our world from the formal description (the "bird's view") of the mathematical structure, and argued that although much work remains to be done here, promising first steps include computing the automorphism group and its subgroups, orbits and irreducible actions. We discussed how the importance of physical symmetries and irreducible representations emerges naturally, since any symmetries in the mathematical structure correspond to physical symmetries, and relations are potentially observable. The laws of physics being invariant under a particular symmetry group (as per Einstein's two postulates of special relativity, say) is therefore not an input but rather a logical consequence of the MUH."
Thomas Howard Ray replied on Jan. 12, 2014 @ 16:13 GMT
It's straightforward, Akinbo. As Max Tegmark explains, after noting that the manifold R, metric space R, number field R and vector space R occupy four symmetry groups in a single representation, "Quantities with units may instead correspond to the 1-dimensional vector space over the reals, so that only ratios between quantities are real numbers."
In other words, the universe of relations among dimensionless points is a real structure independent of internal thought processes. Max's philosophy is an extreme realist position, which I share.
In other words, the universe of relations among dimensionless points is a real structure independent of internal thought processes. Max's philosophy is an extreme realist position, which I share.
Thomas Howard Ray replied on Jan. 11, 2014 @ 14:28 GMT
Florin,
I think you have a fundamental misunderstanding of relativity.
You write: "How is special theory of relativity derived? One starts with the invariance of the laws of nature to changing inertial reference frames. From this you get either the Lorentz transformation or the Galilean transformation, and use the second postulate, that of the constant value of the speed of light, to select between the two choices."
Special relativity is derived from Newtonian mechanics and the Galilean transform, to the limit of the speed of light. One doesn't choose between Galilean and Lorentz transformations -- the domain is continuous. This is important, because it begs the continuity of space with time; i.e., special relativity generalizes to accelerated motion (general relativity) because inertial frames are *not* invariant ("all physics is local").
"But are the laws of nature invariant only to changes in inertial reference frames? How about a trivial invariance: the laws of nature do not change during time evolution?"
However, also because inertial frames are invariant only under the mathematical artifacts of spacetime transformation, whether Galilean or Lorentzian, time does not evolve with the state evolution of invariant inertial frames. This is, in fact, what keeps quantum mechanics from being a mathematically complete theory -- the assumption that t = 1, a trivial constant. The laws of nature are in fact invariant under *space*time evolution.
Tom
I think you have a fundamental misunderstanding of relativity.
You write: "How is special theory of relativity derived? One starts with the invariance of the laws of nature to changing inertial reference frames. From this you get either the Lorentz transformation or the Galilean transformation, and use the second postulate, that of the constant value of the speed of light, to select between the two choices."
Special relativity is derived from Newtonian mechanics and the Galilean transform, to the limit of the speed of light. One doesn't choose between Galilean and Lorentz transformations -- the domain is continuous. This is important, because it begs the continuity of space with time; i.e., special relativity generalizes to accelerated motion (general relativity) because inertial frames are *not* invariant ("all physics is local").
"But are the laws of nature invariant only to changes in inertial reference frames? How about a trivial invariance: the laws of nature do not change during time evolution?"
However, also because inertial frames are invariant only under the mathematical artifacts of spacetime transformation, whether Galilean or Lorentzian, time does not evolve with the state evolution of invariant inertial frames. This is, in fact, what keeps quantum mechanics from being a mathematically complete theory -- the assumption that t = 1, a trivial constant. The laws of nature are in fact invariant under *space*time evolution.
Tom
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