Hello Sean,
Fun paper and great to see a fan of time here!
"Our conclusion that the Hilbert space of the universe needs to be infinite-dimensional might not seem
very startling; the universe is a big place, why should we be surprised that it requires a big Hilbert space?"
Moving Dimensions Theory can provide an infinite number of dimensions. As the fourth dimension is expanding relative to the three spatial dimensions at the rate of c, manifesting itself of spherically-symmetric expanding spheres of locality, each tiny sphere of expansion can be considered a brand new, compactified dimension. Have you ever wondered why photons never, never interact? Because each one travels in its own dimension, as photons are but matter surfing the fourth expanding dimension.
Picture every point becomeing a sphere in the fourth dimension, which yet defines a single locality--the very source of Huygens' principle, which pervades of all nature, from Feynman's many paths to Young's double slit to classical wave pools.
http://jac_leon.club.fr/gravitation/images/kaluza-klein.gif
Feel free to use MDT as a *physical* mechanism to provide your theory with the infinite dimensions you need.
http://fqxi.org/community/forum/topic/238
MDT already provides a *physical* mechanism for entropy, quantum entanglement and nonlocality, all of relativity, all the dualities--space/time, mass/energy, and space/time--so you might as well use it too. :) MDT also accounts for the graviational slowing of light and time, as well as the gravitational redshift, while showing why there is no need to quantize gravity, which will save us all a lot of dead-end work. Please find MDT's treatment of the gravitational slowing of light and time attached.
In his 1912 Manuscript on Relativity, Einstein never stated that time is the fourth dimension, but rather he wrote x4 = ict. The fourth dimension is not time, but ict. Despite this, prominent physicists have oft equated time and the fourth dimension, leading to un-resolvable paradoxes and confusion regarding time's physical nature, as physicists mistakenly projected properties of the three spatial dimensions onto a time dimension, resulting in curious concepts including frozen time and block universes in which the past and future are omni-present, thusly denying free will, while implying the possibility of time travel into the past, which visitors from the future have yet to verify. Beginning with the postulate that time is an emergent phenomenon resulting from a fourth dimension expanding relative to the three spatial dimensions at the rate of c, diverse phenomena from relativity, quantum mechanics, and statistical mechanics are accounted for. Time dilation, the equivalence of mass and energy, nonlocality, wave-particle duality, and entropy are shown to arise from a common, deeper physical reality expressed with dx4/dt=ic. This postulate and equation, from which Einstein's relativity is derived, presents a fundamental model accounting for the emergence of time, the constant velocity of light, the fact that the maximum velocity is c, and the fact that c is independent of the velocity of the source, as photons are but matter surfing a fourth expanding dimension. In general relativity, Einstein showed that the dimensions themselves could bend, curve, and move. The present theory extends this principle, postulating that the fourth dimension is moving independently of the three spatial dimensions, distributing locality and fathering time. This physical model underlies and accounts for time in quantum mechanics, relativity, and statistical mechanics, as well as entropy, the universe's expansion, and time's arrows."
In your essay, you write, "But the proof of the pudding is in the tasting, and right now the best taste we have of quantum gravity comes from string theory."
This is kind of like saying the best taste we have of traveling faster than light comes from the Millenium Falcon in Star Wars. Since string theory has no equations and is not a finite theory of anything, and since quantum gravity exists neither in theory (nobody has one, nor has come close) nor in reality (nobody has ever seen a graviton, nor knows how we might look for one), I guess it makes sense that the best way to taste quantum grvaity (which does not exist) is with string theory (which isn't a theory). But going after what might not exist with what never works in finding what might not exist just doesn't seem fun anymore. Even John Baez is leaving his pursuit of quantum gravity behind ( http://www.edge.org/q2008/q08_5.html ), and perhaps the time is nigh for all of us focus on Movindg Dimensions Theory with multi-million dollar initaitves, as MDT provides a *physical* mechanism and model for time and all its arrows and assymetries, as well as entropy, relativity, and quantum mechanics's entanglement and nonlocality.
I enjoyed the sentence, "(Juan Maldacena) discovered that a four-dimensional supersymmetric gauge theory defined on Minkowski space, in the limit of a large number of colors and strong coupling, is equivalent to ten-dimensional supergravity compactified on a fivesphere, with anti-de Sitter boundary conditions at spatial infinity."
Well Newton dicovered gravity, and Einstein discovered relativity, and it seems Shakespeare was right--brevity is the soul of wit.
Do you not long for the heroic age of physics, whence physics was explained in terms of simple, physical concepts, with simple mathematical equations?
Do you not long for simple postulates reflecting *physical* truth: the fourth dimension is expanding relative to the three spatial dimensions at c, with simple equations: dx4/dt=ic, and far-reaching conseuqences, as diverse physical phenomena spanning all realms are united with a simple model?
You write, "When quantizing gravity, spacetime itself becomes part of the quantum description, and time seems to disappear according to the Wheeler-DeWitt equation."
Well, actually, nobody has ever quantized gravity. So how would we know what happens when gravity is quantized?
You write, "But the Schr¨odinger equation, on which this is all purportedly based, is perfectly reversible."
Actually, if one uses the Schrodinger equation to describe radiation, it does not describe a reversible process, as radiation in its simplest case appears as spherically-symmetric waves that are expanding, not shrinking. this is because photons surf the fourth dimension, which is expanding, not shrinking.
wiki page
http://en.wikipedia.org/wiki/Photon
You write, "But the reason why we ever had access to a low-entropy configuration such as an egg is ultimately because the environment of the Earth is a low-entropy place."
Actually the creation of the egg in the chicken increased the entropy of the universe. I'm not sure I agree that the solar system is a low-entropy place--compared to who's absolute rule/measuring stick of entropy? It might have lower entropy than other places, but does that it make it a low entropy place? It is what it is. What should it be if not what it is? And cans such questions be answered by science?
You write, "But the fact that we ever began with a low-entropy is not natural at all." Did not the solar system and earth evolve from a swirling cloud of dust over billions of years? Was the entropy of the swirling cloud of dust so very low?
All these quotes are great, but are they science?
Is expressing and re-expressing the anthropic principle science? We are here because we are here and if we weren't here we woudln't be, so there must have been a statistical deviation. This is nothing new. Had our parents nver met, nor theirs, nor theirs, nor theirs--what are the chances? We owe our DNA to a vast improbability. OK, now let's move on to asking and answering foundational questions about *physical* reality.
Are tautological witticisms science?
"A universe containing mathematical physicists will at any assigned date be in the state of maximum disorganization which is not inconsistent with the existence of such creatures."
You write, "In fact, entropy can grow both into the far future and into the far past; the overall multiverse can be
completely symmetric with respect to time."
Can entropy really grow into the past?
MDT shows that the past isn't real, as the block universe does not exist.
And if you suppose a block universe, the past is frozen, so its entropy can't change there either.
Have to run! Thanks for the words!
Best,
Dr. E (The Real McCoy)Attachment #1: 6_MOVING_DIMENSIONS_THEORY_EXAMINES_THE_GRAVITATIONAL_REDSHIFT_SLOWING_OF_CLOCKS.pdf