The metaphysics, or analytical mathematircal philosophy, baseically is that any scheme for causality is going to be incomplete. It will not be able to encode all possible physical states. As a result it means there exists a deeper foundation to the universe. In the second half of this paper I argue this involves the associative property of the vacuum with respect to quantized event horizons.
Cheers LC
Thanks for the reply.
"baseically is that any scheme for causality is going to be incomplete. It will not be able to encode all possible physical states"
In which physics problem this problem appears. Is it in scattering s-matrix or in describing proton wavefunction. I mean EXACTLY which physical problem you are having trouble solving because of this issue. Sorry for repeating my question, I hope I am more clearer this time.
Hi Lawrence,
I do not believe that LQG /CLQG is a serious candidate for quantum gravity and it is not my favorite. In LQG the space is granular (a network of finite loops) and this is contradictory to my view of continuous spacetime. However I like its evolutionary aspect in the sense of SOC and the scale-invariance that is crucial to fill the gap between GR and QM. I have mentioned LQG / CLQG only for reference to your determinism in a "clockwork" and evolution. After all the evolution notion is used very often by physicists but usually in the common meaning as a process of a change e.g. stellar evolution. But this has nothing to do with self-organized criticality. I would like to apply Darwinism beyond its original sphere of organic evolution on Earth using SOC.
I like the extremal principle in a sense of non-equilibrium thermodynamics to look for the likely steady states. This is also a kind of evolution of a far-from-equilibrium system to a steady state.
String theories do not generate predictions so they are non-falsifiable.
And finally I am sorry but the language of modal logic is not my 'mother tongue'... just like English. Maybe I should start to learn...
The situation pertains when there is an uncertainty fluctuation of event horizons. This is a possible window into quantum gravity. The physical states in the S-matrix channel are entangled states, with entanglements across the horizon. If the event horizon is classical then everything is nicely associative. A fluctuation in the horizon results in this uncertainty in associating states interior and exterior to the black hole/
The graviton has quantum numbers equivalent to an entangled pair of QCD gluons, or a bi-gluon system, that is neutral with respect to color charge. In that sense this form of S-matrix does connect in formalism with the old S-matrix theory or the so called "bootstrap." In fact string theory is really that unitary bootstrap theory in another guise.
I hope this answers your question.
Cheers LC
I think spacetime is continuous or granular depending upon which sort of measurement you make. The Planck scale is just the minimal length scale which can contain a qubit of information. Space or spacetime on a smaller scale can not contain a qubit with any certainty. An experiment that involves the transmission of information over a vast time distance has no uncertainty with respect to the existence of it information or qubit content due to quantum gravity. As a result spacetime appears perfectly smooth. An experiment on the other hand which attempts to localize a very small region of space, say at high energy, will then register a different perspective on spacetime. In that setting it may appear highly choatic and granular.
The predictions of string theory involve cosmology and black holes. In a stringy universe there are some observable consequences, in particular with respect to multiple vacuum nucleations or bubbles that we call a "universe." Signatures of this may be imprinted in the fine grain detail in the CMB anisotropy. The graviton has quantum numbers equivalent to an entangled pair of QCD gluons, or a bi-gluon system, that is neutral with respect to color charge. This means that plasmas of gluons can be formally equivalent to a black hole. In a funny way it is a black hole. So holographic physics should in principle be testable in heavy ion collisions. These are admittedly rather indirect or oblique sorts of tests, and even if confirmations of string predictions are found the whole string-M/theory enterprise is likely to remain on rather unsteady ground.
The real problem is that we appear to be reaching a sort of ceiling of technological possibilities. One of these is of course directly testing Planck scale physics. Other limits seem to be with high density energy sources such as fusion, that seems as remote as ever, the future of manned spacetravel appears in trouble, and there are slow downs with Moore's law with computers. We also need to consider the pile up of huge problems like global warming. We may be approaching the end of the foundations of physics because of our limitations.
Cheers LC
Dear Lawrence,
I agree we are hitting the technological limits within contemporary experimental physics. However there is a hope - a new idea falsifiable with a simple experiment. I have proposed one that could be even an exercise for students. But to carry out the experiment we need someone who is ready to risk his authority like J.A.Wheeler.
Best regards
I am slowly making my way through the essays. I have not yet gotten to yours. Are you proposing this experiment in your essay? I will try to get to yours in the next few days. I can only read one of these papers in a day, so it is a bit slow going.
Cheers LC
Dear Lawrence,
In my essay I have only mentioned the spin experiment but in references you can easily find a link.
I just pulled up your essay and gave it a quick reading. It is not terribly long. It appears that you are asking whether certain properties are physical or geometrical. At this time I don't have an assessment of your work. I will need to read a bit more.
Cheers LC
Hello Lawrence Crowell,
First off, I'd like to say I like your style, and the way that you seem to put issues in their proper perspective! It brings a calming sense of reason to an area of question that retains so much hype that it no doubt triggers numerous thoughts every time one hears Q.M. and locality are mentioned. Secondly, I don't think determinism should dictate the development of a new theory. It, as your historical view has made clearer to me, is an idea used to adapt old world views into current problems.
About the idea that the computer, either a real one or the universe as one idea, being faulty because it doesn't model the entire set of events, could it be that this is not against saying that there is a separateness between real entities in space which unaccounted for doesn't describe all events in the universe? Or, does a clock here have to do with one spatially separated over there? Not being mathematically trained enough to see clearly the math in or around the black holes, I will leave this comment with one question only. As an aside, I'm glad to hear someone say "bottom-up" once in a while.
Best,
W. Amos Carine
The relationship between events in the universe and causality was noted by David Hume to not have a strict logical relationship. As I indicate in a footnote Godel's second theorem according to modal operations is a form of Hume's argument about causality =/= logic.
I sort of have to make this a bit brief due to other things I have to attend to now. I will say that the issue of clocks with a spatial separation and synchronization is a subject of considerable interest. This involves Cauchy data on spatial surfaces and how to integrate the Einstein field equations.
Cheers LC
Thank you Lawrence C. for giving me something else to look into!
I agree with you that the universe computes itself and thus discovers itself. I've presented an argument that supports this view. According to this argument Plancks constant h is nothing else than the physical expression of something which is commonly known as "natural digit".
The self computation of the universe probably leads to this Turing-Godel limit with Lambda calculus. There is clearly a computational aspect to the universe, which is a causal structure.
I will take a look at your essay soon. The Planck constant is in naturalized units just "one," and does probably reflect a unit of of natural numbers that sum up to give the total action. I notice yours seems to be in the latest introduction of new essays.
Cheers LC
Lawrence,
When reading; "A model of the physical universe encoded by algorithmic means will not compute reality" I suspected I may enjoy reading your essay. I was right.
You present a very level and balanced view, and more readable by the target audience than previous years. I do suggest something rather radical regarding that above sentence myself!
I also found other resonances with mine; "It is entirely possible this could be used to argue for a 'top-down' physics with the emergence of higher level properties." which I identify in terms of higher 'sample spaces' and subsets and test against the EPR paradox.
I also agree your analysis; "GR is a geometric theory of spacetime, which means that quantum gravity is quantization of spacetime itself. It is not entirely clear what this means. A number of questions have to be answered, and currently there are obstacles in our current theories which do not permit us to address these issues well."
But are the apparent 'obstacles' it not only 'assumptions'? so testing other assumptions may be fruitful (without the feared ether), i.e. that quantized atomic scattering to c maintains the SR postulates locally, (the LT then emerges naturally as a know optical effect).?? (You may recall from my last years effort how modal logic applies to that case).
I hope you can read mine and look forward to your and comments. I'm sure you'll stay in a more elevated position this year.
best of luck.
Peter
Hi Peter,
I am true to my usual trend falling behind in reading papers on this list. I just did a scan of your paper. You do reference Godel's paper on prepositional logic. The main point of my work is that any Lambda-calculus or Turing machine approach to the structure of a causal system is bound to be incomplete. I do get a sense in reading the first couple of pages of your essay that you are leading into something similar.
I probably will not get to reading papers much until this weekend. I'll post my observations when I do. As I said I am falling behind, and I notice another lot of papers showed up on the list today.
Cheers LC
Hi Lawrence,
I've just had a complete read and I really enjoyed your essay. The quantum nature of information does seem to point towards us concluding that neither it nor bit are more fundamental. I reached a similar conclusion in my essay. I particularly like the idea that this may have applications in consciousness.
Regards
Antony
Hi Lawrence,
a very interesting essay, I enjoyed to read it. It seems (again) that our approaches are related (see my essay). I also claimed about that the information contained in spacetime is undecidable (by the word problem in group theory).
More later after rereading your essay
Torsten
Hi Torsten,
I remember reading an article back in the 1990s about how the classification of exotic R^4s was not enumerable, which had connections to Godel's theorem.
The exotic R4 structure has its origin in the Casson handles as pointed out by Freeman. A thickened disk D^2 --- > D^2xR^2 can produce various structures, which by the self duality of four dimensions leads to these strange conclusions. In scanning your paper I see you invoke Casson handles. The number of such structures by h-cobordism turns out to be infinite, which as I say above, I remember this to be nonenumerable. This result was proven by one of the big mavens in this area, Atiyah, Freeman, Taubes, ... ?
The one element of this is that the e8 Cartan matrix as the eigenvalued system for an E8 manifold, an exotic R4. It has been a while since I have studied these matters, but as I remember this tells us how to tie 3-manifolds in 7 dimensions in the Hopf fibration S^3 --- > S^7 --- > S^4. The dual to this structure are 4-manifolds. The 7 manifold this knotting is performed is in the heterotic S^7 --- > S^{15} ---- > S^8, and the e8 Cartan matrix gives the eigenvalues for the 7-space.
The interesting thing about the E8 is that the 8-dimensional space is equivalent to the group in a lattice construction; the root-weight space is ~ the space itself. The E8 manifolds of Freeman are I think embedded in the set of possible 8-spaces. This suggests a duality between the smooth manifold in 4-dim and a discrete or noncommutative manifold in a quantum sense.
Physically this seems evident from data obtained so far. Measurements of the dispersion of light from extremely distant sources invalidate a discrete structure to spacetime. This tells us that a measurement of spacetime structure by measurement of photons that traverse a large distance give no signature of grainy structure. Yet a lattice perspective of spacetime with the Grosset polytope and the 120-polytope of quaternions in 4-dim would suggest a noncommutative geometry. However, if the lattice is equivalent to the space, then this smooth structure is dual to a grainy picture of spacetime. This structure should emerge in an extremely high energy experiment that probes small regions, rather than testing across vast distances.
Cheers LC
The icosian or 120-cell has two quaternions with length (1/2)(1 +/- sqrt{5}) where the plus one has length 1.618..., which is the golden mean. In fact these quaternions define something called the golden field in a Galois ring. This is related to the Fibonacci sequence.
Cheers LC
