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Author
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Topic: Universal Memory and Quantum Gravity
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chimp
Member
Member # 333
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posted 04. October 2003 17:33
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Russell,
I did want to add one comment to your (creative) idea that the universe acts as its own holographic memory. You use a blackhole as the baseline of your analogy. As I understand it, a black hole has an "event horizon," beyond which light cones cannot go (thereby providing a template for "memory" of those light cones).
However, as Hawking describes it, the universe, though finite, has no boundary (that is, no "event horizon"). It seems this "no boundary" condition of the universe therefore fails to provide the template for any universal memory. Do you think this contradicts your analogy?
Quantum mechanics leads us to the realization that all matter-energy can be explained in terms of "waves". In a confined region(i.e. a closed universe or a black hole) the waves exists as STANDING WAVES In a closed system, the entropy never decreases.
The analogy with black holes is an interesting one but if there is nothing outside the universe, then it cannot be radiating energy outside itself as black holes are explained to be. So the amount of information i.e. "quantum states" in the universe is increasing. We see it as entropy, but to an information processor with huge computational capabilities, it is compressible information.
Quantum field theory calculations where imaginary time is periodic, with period 1/T are equivalent to statistical mechanics calculations where the temperature is T. The periodic waveforms that are opposed yet "in phase" would be at standing wave resonance, giving the action.
Periodicity is a symmetry. Rotate into the complex plane and we have
real numbers on the horizonal axis and imaginary numbers on the
vertical axis. So a periodic function could exist with periodicity
along both the imaginary AND the real axis. Such functions would have
amazing symmetries. Functions that remain unchanged, when the complex
variable "z" is changed.
f(z)---->f(az+b/cz+d)
Where the elements a,b,c,d, are arranged as a matrix, forming an
algebraic group. An infinite number of possible variations that
commute with each other as the function f, is invariant under group
transformations. These functions are known as "automorphic forms".
Topologically speaking, the wormhole transformations must be
invariant with regards to time travel. In other words, by traveling
backwards in time, we "complete" the future, and no paradoxes are
created.
So when spacetime tears and a wormhole is created, it must obey
certain transformative rules, which probably appear to be
discontinuities from a "3-D" perspective, but really, these
transformations are continuous!
So the number of holes[genus] on the surface of space, determine
whether there exist an infinite, or finite, number of solutions to
the universal equations?
Multiverse, or one Universe?
Strong Anthropic Principle or Weak Anthropic Principle?
All elliptic curves are modular.
We are automorphic forms.
quote:
Also, you stated:
quote:
Actually spacetime does not need to be "sliced up" in that it can proceed in discrete steps, yet still be continuous.
I agree that spacetime is continuous. This is one of the central postulates of science. I don't necessarily agree that spacetime proceeds in "discrete steps." I think "discrete steps" reflects the reductive tools we use to analyze the natural world, and it does not necessarily reflect the natural world itself (or, at least, all of it).
Just an offhand rhetorical example: Please describe the "discrete steps" of an electron as it passes through 2 slits at the same time.
When an electron moves to a lower energy level in an atom, its "quantum jump" is a discrete step.
[higher energy level]--->[lower energy level] = discrete step ![[Wink]](wink.gif)
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I think we use "discrete steps" because it is harmonious with our common sense notion that one event follows on another in an orderly, cause and effect way. Would you agree that QM challenges this notion?
Energy is quantized according to the equation, E = hf
Read about the "ultraviolet catastrophe":
http://www.wikipedia.org/wiki/Ultraviolet_catastrophe
http://spiff.rit.edu/classes/phys314/lectures/planck/planck.html
We must use discrete steps. But those steps can still be causally connected i.e. continuous.
[ 04. October 2003, 17:41: Message edited by: Russell E. Rierson ]
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chimp
Member
Member # 333
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posted 05. October 2003 04:25
The information density of space increases. This is a relation and its inverse.
For example, unity is a constant, representable by:
[1 = c ] = [1/2 + 1/2] = [1/4 + 3/4] = [1/5 + 4/5] = [1/6 + 5/6]
The left fraction represents [energy/momentum] and the right fraction represents compressed [space/time] density, where space means "distance interval" , a relative measurement.
[E/p]<--->[S/T]
[1/R]<--->[R]
The physics for a circle of radius R, is the same for a circle of radius 1/R
E/p = S/T = c
[Space/time] and [energy/momentum] are two different forms of the same invariant quantity [c].
[E/p]_n = [E/p]_n+1 = [S/T]_n = [S/T]_n+1
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chimp
Member
Member # 333
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posted 06. October 2003 00:41
Yes, c+c = c
[c + c]/[1 + c^2/c^2] = c
So E/p + S/t = 2c/2 = c
S/T = E/p = S/T + E/p = c
We live in a nonlinear universe. Einstein's equations don't lie
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