The Fabric of the Cosmos

By: Brian Greene, read in 2004

29 Newton: Space is the sensorium of God
79 A "self-evident truth" that I doubt: that two birds are distinct
91 We don't know how to envision what QM probability waves are.
99 Bohr: reality = things we can measure
119 Wave function collapse does not emerge from QM math!
128 Conscious experience of time
130 Unwarranted assumption: That we are "all within space-time" and never "outside".
131 Not true! What about dreams?
131 Consciousness embodies what science has been unable to find.
138 All of space-time exists - not just the "now-slice".
139 Conscious experience moves through time.
140 A discussion similar to my "What Might be Going On(?)"
141 He makes my case for additional temporal dimensions.
141 Einstein on the problem of "now" being beyond science.
141 Good discussion demonstrating the separateness of experience & physical laws.
154 Entropy - the definition is incomplete and meaningless without involving consciousness (See Encyclopaedia Britannica 11-258b for a good discussion of entropy, information, thought, brains and life.)
203 Stage 1/Stage 2 QM sounds like Cartesian duality.
216 Needed: time-asymmetric solution to the measurement problem with entropy decreasing toward the past.
220 Error: Cubes are also symmetric wrt diagonal axes for rotations of 120 degrees.
226 Wheeler: "Time is nature's way of keeping everything...from happening all at once".
232 The pennies-on-balloon analogy doesn't account for constant penny size or for the extra (large!) dimension of space it requires.
236 Greene dodges the extra-dimensional implication calling it "meaningless".
237 His explanation of fixed penny size. Suppose the pennies grow. From page 46 and 229, stretching speed per mile of separation = 5.5 million mph / 100 million light years = 9.27X10-15 mph/mile [should double check these calculations.] = .0000052 inches per year per mile! That would be easy to overlook.
242 I don't think a "saddle" shape is "completely symmetric"; curvature is different for different directions.
253 Inconsistency with note 2 p517. Confusing order and symmetry.
286 Leibniz: "Why is there something and not nothing?"
310 Greene: Logic alone predicting physics is a "pipe dream".
314 Entropy-as-order seems unjustified to me.
317 Is chicken feed more "ordered" than a chicken? I doubt it.
321 Good, short, summary of inflationary cosmology.
333 While we're at it, why not consider "space itself" to be an embedded manifold?
355 Super-symmetry or super string theory ~ integer and half integer spin symmetry.
359 String theory requires 10 space-time dimensions.
360 Greene claims that Theodor Kaluza was German. Not Swedish?
361 Kaluza's insight re Einstein's & Maxwell's equations.
361 Greene: Inability to detect hyperspace is a "problem".
361 Kaluza learned to swim by reading a book.
361 Oops! It was Klein who was Swedish.
362 Tightrope analogy is bad: "easy to see", by whom? Philippe? worm? distant observer?
362 The tightrope's surface is a manifold and not a dimension.
363 Fibers do not have "circular dimension" except as a new set of basis vectors defined on a manifold.
365 Not quite! The circles on the tightrope have no extension in any dimension of the tightrope; in Fig 12.7 they have extension in one of the dimensions of the fabric.
365 Implication that curled-up dimensions are necessary to escape detection.
366 The answer to "why the universe [has 11] dimensions" may be that we are at that point in cosmic evolution. The number of dimensions, along with cosmic complexity, may be evolving.
369 Calabi-Yau spaces.
372 Particle properties depend on C-Y spaces. I say why not as C-Y manifolds?
372 "Since we don't see the extra dimensions, they must be small".
373 The significance of the number of holes in a C-Y space.
374 Extra dimensions may hold the key to the deepest mysteries.
374 Inflation may have been asymmetric wrt dimensions.
382 Kaluza showed that 5 dimensions unifies gravity and electromagnetism.
383 "historical pattern of achieving unity through more dimensions"
383 "The known equations are still unable to nail down the sizes or shapes of extra dimensions".
385 Strings (1-manifolds) necessarily include gravity where points (0-manifolds) = electrons, photons, etc.
392 "Why don't we see the three-brane...?" We do; that's all we see.
393 YES!! That's what I've been saying all along! We shouldn't expect to be able to see extra dimensions!
394 Giant leap to assume "everything we've ever seen" is "everything".
412 Greene: There may be much more to reality than 4D space-time.
441 Assumption that consciousness is seated in the brain.
441 In a human body, a trillion atoms are replaced every microsecond.
452 Greene: an observer following a static world line is not logical. I think it is.
475 The "need" to curl up extra dimensions.
475 If the particular "size and shape" of dimensions in Type IIA and Type IIB theory were seen as manifolds and not dimensions, then their geometries would naturally differ if seen as orthographic projections. That explanation would seem to be a lot more natural and simpler.
477 Re two observers using different string theories and concluding that space has a different size and shape for each, he says: "Note too, that it's not that they would be slicing up spacetime in different, equally valid ways, as in special relativity." I say, Why not? That would seem to be a better interpretation to me.
478 Definition of 'entropy' requires an observer with assumptions on acuity.
479 I suspect that this line of reason is fallacious.
479 I thought so!
480 This paragraph sounds like baloney.
481 Sounds to me like Greene has described a manifold and not a hologram.
482 Yes. That's another way of saying we live in a 3D manifold embedded in 4D space.
483 Tacit declaration that string theory requires curled-up dimensions.
483 Interesting! This suggests a possible mechanism for evolving a cosmos of successively more spatial/temporal dimensions along the lines that I envisage.
484 Yes! Just as a manifold and its boundary are on equal footing!
485 Yes! It suggests the possibility of cosmic evolution with increasing number of dimensions.
487 "background-independent" formulation ~ spaceless-timeless formulation
490 Could the "loops" be information storage delay loops? This could possibly lead to a fractal generation of the fabric.
491 Do "relative relationships" have any meaning in the absence of consciousness? I don't think so.
492 Maybe not: Individual experience may frame space and time!
496 Maxwell's equations.
498 Einstein's field equations.
499 Greene: Spacetime = manifold + metric.
505 The Minkowski space-time metric.
506 Time reversal and CPT asymmetry of weak interaction.
512 Schroedinger's Wave Equation
516 Calculations of light travel along null geodesics of the metric
526 The assumption that all known fields exist "everywhere" is either unwarranted or misleading. It is possible a field may exist only in a particular manifold. e.g. ocean waves exist only on the surface.
526 A dead-calm ocean is different from no ocean.
527 The time variable disappears when GR is transformed in a straight-forward way by QM!! This suggests to me that the temporal dimension we "experience" might, in reality, be another spatial dimension which is part of our 4D manifold and which is traversed, in a higher temporal dimension, by a conscious agent.
529 Strings conform to infinite symmetry groups. Higher-D branes conform to finite symmetry groups. Greene implies this is a negative; I think it is a positive feature.
530 I believe Dr. Dick has proved that any consistent formulation of a description of fundamental reality must conform to QM rules.
530 I suspect that "winding" is not a good explanation for T-duality. It seems more likely that the brane is spherical so the duality is due to the interchangeability between inside and outside. If R is the inside radius, then 1/R is the antipodal radius.
534 I don't buy this demonstration of additivity of entropy. This would hold if there remained a partition between the two tupperware containers, but not otherwise.
535 It seems to me you would have to admit (astronomically) large extra spatial dimensions to be able to talk about "light sheets". in this way.
536 This either sounds like nonsense, or it begs a definition of "spatial infinity".

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