Duality in Cosmology and the Limits to the Acquisition of Information by Lawrence B Crowell

James Hoover

Lawrence,

"The main point of my article is that it is not likely for intelligent life or IGUS to develop into these hyper-civilizations. It does not mean that intelligent life is doomed utterly, but it does mean such is limited and will pursue a better future if they work within or around these limits."

My question relates to whatever humanity may be out there, yet undiscovered. Evolved differently than us, would that intelligent life achieve hyper-civilization, and in fact if they have already visited us -- undiscovered -- wouldn't they already have achieved a "hyper-civilization? I know it's speculation but that is what we are doing with our subject.

Jim

Lawrence Crowell

The main argument I make is that it is physically improbable, if not maybe impossible, for these extreme hyper-civilizations to exist. The problem is that they can't acquire energy and information necessary to do this. The primary limitations are the finite speed of light and the existence of cosmological event horizons. This is then my argument for why our observable universe is not some sort of simulation run on a hypercomputer built by some extreme IGUS.

I doubt that we have been visited by any sort of extraterrestrial intelligences. I suspect the distances are not just interstellar, but probably intergalactic. So such travel is unlikely. I prefer to use the ter IGUS for such beings, for I doubt they will in any way resemble humanity. They will probably assume a form and consciousness states that are hugely different than our selves.

James Hoover

Lawrence,

I hear you about the limit of light speed, but even with our existing Type 0 civilization we leave the door open to warp speed and the fabric of space exceeding light speed. I would wonder if you leap ahead to a type 2 civilization whether that light speed limit evaporates with access to Planck sizes and quantum access. Does quantum entanglement give you access to entangled particles light years away. I know orthodox physics frowns on this but look how perspective has changed in a few generations.

Jim

Lawrence Crowell

The speed of light is not the same as the speed of sound. The speed of light is a conversion factor between time and space. It is also in relativity a consequence of the spacetime distance or interval for a photon is zero. This means that the set of light rays in spacetime defines a projective geometry. Projective geometries are a set of rays or lines modulo length. Zero length photon rays are the perfect example of this type manifold. The speed of light is then a manifestation of topology as well as geometry.

Event horizons are congruencies of null rays, null rays being zero length paths that light or photons follow. The trapping properties of horizons are then a sort of invariant or topological property. The actual speed of light is not relevant. In fact the natural unit for the space of light is just one or c = 1light second per second. The funny units we see for it is then due to other parameters or constants, such as the electric charge or the mass of particles.

The invariance of the speed of light is a local property, or it operates for local inertial frames. The global manifold with curvature has different regions with local light cone conditions. The question of course is whether the causal condition of local invariance of speed of light holds globally. This depends upon whether a number of conditions are upheld in general relativity, in particular the Hawking-Penrose energy conditions. There are good reasons to think these hold, even in quantum conditions. However, as yet a proof does not exist.

KoGuan Leo

Lawrence,

I enjoyed reading your essay full with equations. I understand your view about natural world as it is is is. Even when you used mathematical equations which use few symbols to simulate natural world you still claimed as Seth Lloyd did that our universe simulates itself, or we need a universal size computer to simulate our natural universe. How come you need you to use few symbols to simulate some versions of Existence in this essay?. Why don't you use the actual world to express actual world? Of course you would say this is not possible to put natural world onto a virtual 2D computer screen. Is this not a paradox that mathematical symbols can express the natural worlds as it is like the Newton's ma = GMm/r^2 that helped us to put man on the Moon? Or Maxwell famous four equations that simulate our natural electricity and radio signals in our virtual mobile phones that we as the hard nosed realists find cannot live without? And so on. Also our collective consciousness acceptance of our matrix money does simulate actual money that we use as our means to transform virtual values into actual exchange values in the market system. Why can't we just use actual house to trade with another actual house? Again the answer is obvious, it is not practical and not efficient to do so. We exchange our stimulated virtual money with actual house. Yes a few symbols can simulate actual reality which is fiction but real. KQID reveals that our one and only Ancestor FAPAMA Singularity Qbit (00, +, -) computes, simulates and projects Einstein complex coordinates (iτLx,y,z, Lm) onto the two D time screen and then into the three D time in time. Yes we do live in the 3 D Matrix world that is naturally seamless and perfect as we find it as it is and this is is is that is fiction but real. Yes our Multiverse is the fetus of Lm, our Multiverse timeline, and this timeline Lm in the zeroth D is pregnant with our Multiverse. This Multiverse timeline Lm in the zeroth dimension is nothing other than our Ancestor FAPAMA Singularity Qbit (00, +, -). Yes we are living in a real reality that is fiction. This fiction is real to us. Just like virtual money in our virtual matrix world is real to us. Why? The same reason. It is practical and efficient for our Qbit to compute, simulate and project Existence from its bosom to our natural real world. These phenomena are happening right now in front of our noses. It is just too obvious to be noticed, like a goldfish finds itself naturally in a real world inside its fish bowl.

To avoid misunderstanding, I agree with many of your conclusions except those that I pointed out above. I always enjoyed your essays. They are always profound with thought provoking ideas. I want to read more of them. Best regards, Leo KoGuan

Lawrence Crowell

Dear KoGuan,

Thanks for your interest in my paper. There is clearly a quantum bit/logic component to the universe. Any physical system with a set of conservation laws is in a sense a "computer." A conservation law is equivalent to a symmetry principle, by Noether's theorem, and a symmetry principle gives a set of precise rules for the transformation between states. This has algorithmic aspects to it. However, I tend to avoid making a sweeping declaration that the universe is a computer. Of course that could be the case, and which does mean the universe computes itself. The computer is in effect the program and data stack. I think there are elements of this in the physical universe. However, again I avoid making a grand generalization that says the universe is a computer.

KoGuan Leo

Dear Lawrence,

Fantastic essay indeed! You wrote powerfully and wonderfully: "The question in the end is whether this in fact might be a good thing. We are in age where the ability to simulate the world is very advanced, and will advance much further. Further, the interface between human brains and computers is becoming very close. For an overview of the brain-computer interface (BCI) see [3]. BCI is an experimental science and it is a matter of time before this is commonplace. People will before long embrace this eagerly, just as people now spend many hours a day on smart phones. It means soon the ability to simulate the world and to experience that virtual world directly through the brain will become reality. At some point the human mind itself might be simulated or uploaded into a cyber network. The distinction between reality and virtual reality could well become increasingly lost in the near future. It may then become questionable whether the entire universe we observe is not some grand simulation. The game masters might be humans, or they might be other extraterrestrial life forms, and we may be avatars in this game, much as with the move "The Matrix."Without limits on this sort of development we canË†at know whether the world we observe is ultimately just a computer game run by unseen programmers or superagents."

Please forgive me to put my writing in your blog, because I respect you are as a great and creative scientist. However, I may be too "bold" to you. I see no limit in our simulated reality, although I believe the reality is simulated by our Ancestor FAPAMA Singularity Qbit (00, +, -). We are avatars of our Ancestor. Thus, even if we humans or our descendants who would actually do the simulation from KQID perspective it is still our Ancestor Qbit through us or our descendants would actually do it. Here below if I may state it briefly quoted from my another writing:

"Our Ancestor FAPAMA Singularity Qbit (00, +, -) Â emerges from Non-existence by its own free will to exist based on KQID Giving first and Taking later principle as the founding omni-principle that creates and distributes Existence. Using this KQID founding principle, it wills itself to emerge from Non-existence.Â Therefore, the Giving first Taking later founding omni-principle is actually the Qbit itself. From this founding principle, the Qbit writes the simplest and shortest Founder's algorithmic codes possible to ensure its all possible evolutions for all eternity. The Qbit including its founding codes evolves and adapts itself according to Darwinian natural selection and meme codes mutation to deal with all possibilities and potentialities every absolute digital time Â â‰¤ 10^-1000seconds. I called the Founder's codes: the Zeroth Law: Îž 00 Îž Ee^iÏ„=A+S = IÎ¨(CTE) = Î¨(iÏ„Lx,y,z, Lm) âŠ†T = 1. Existence must be a unitary physical system in the zero dimension, in the zero time and in the absolute zero temperature. It is mandatory that information cannot be deleted nor destroyed to keep itself always forever in the pure state of quantum superposition. Its evolution has to be unitary one in which the total sums of the quantum probability of the whole system is always normalized unitary 1. Our Ancestor Qbit (00, +, -) is the singularity programmer, KQID computer and the projector three in one applying the shortest and simplest possible one line algorithmic formula Â Ee^iÏ„=A+S âŠ†T = 1 to compute, simulate and project Shakespearian meme-actorÂ Î™Î¨(CTE) acting on relativistic stage (iÏ„Lx,y,x, Lm) hologram Multiverse."

Now I can rate your essay and I rated it a ten (10). I really love and enjoy it.

I wish you the best, Leo KoGuan

Lawrence Crowell

Thanks for the high score.

The technology to simulate things and to create virtual worlds has become enormously advanced. The BCI and other developments are probably not far down the road. As you say we may become increasingly lost in a virtual reality as we will not longer be able to cipher what is simulation and what is not. Already with what exists there are many cases of how disinformation and intentional falsity are presented as reality, and I suspect that it will not be long before this becomes the norm, where humanity may becomes inwardly drawn into a mass mind meld. It has disturbing parallels with the motto of the BORG on Star Trek, "You will be assimilated, resistance is futile."

I do think the universe is largely unitary, or in some general unital setting that could be unitary modulo singular points or meromorphic. This unital structure may however depend upon an open or hypercomputational system in black hole interiors and in exceptional situations. Quantum states in our exterior region are entangled with these states and unital structure is maintained by hypercomputation with these exceptional states.

I am even more confident that simulations are capable to performing this type of computation over an arbitrary time period. I did not include this for these hypotheses are rather conjectural at this time. A perfect simulation of this is not possible by the Godel-Turing theorems. Even a "darn good" simulation would require access to a huge amount of mass-energy and information, which becomes problematic in general.

Cheers LC

Wesley Hansen

An interesting paper, Lawrence, although I often wonder, even if our Universe is a simulation, wouldn't it all have to bottom out in "nature" eventually? I mean, the word simulation implies something being simulated and, although I can easily imagine a countably infinite regress of simulations, it would seem the uncountably infinite would, by necessity, include "nature" somewhere within its bowels. Of course, with regards to our current situation and future prospects this could very well be irrelevant, but I wonder . . .

And speaking of virtual reality Turing tests, have you heard of the 11:11 phenomenon? According to my research, many Evangelical Christians believe the 11:11 phenomenon is an indicator of the final days, the beginning of Revelations. So, to prepare, they built a $50 million, family-friendly, Christian theme park next door to Tel Meggido, a. k. a. Armageddon; I'm not really certain as to the objective the theme park is meant to address, but from the bizarre little book, "Apocalypse 2012," by Lawrence Joseph (pg. 180):

"Evangelical Christians are the group most eager to precipitate Armageddon, looking forward to the Rapture, the exalted moment when, before the battle begins, true and faithful Christians are literally lifted up into the air, into the heavens, to join God. No doubt this would be exhilarating. From the safety and comfort of Heaven, one would have the opportunity to look down upon the Earth and watch the battle between two warring groups: Christians who, due to imperfections in their faith, or because of special warrior destiny, were not subsumed in the Rapture; and followers of the Antichrist, a charismatic false Messiah, whose followers include secular humanists, pagans, Hindus, and Buddhists, as well as Muslims, Jews, and insufficiently committed Christians. A large portion of Jews are expected, in Evangelical theology, to convert to Christianity and thus fight on the righteous side of the Armageddon battle. Those who decline Jesus will, along with all other naysayers, explode."

Now if this should come to pass, wouldn't that be like the ultimate virtual reality Turing test? And if this did come to pass, wouldn't it demonstrate psychosis on the part of those responsible for the simulation? This would explain a lot of things . . .

There's a nice interview with Alexandra Elbakyan about BCI technology and trends in the Humanity book, "Between Ape and Artilect", on page 337 . . .

With regards,

Wes Hansen

Lawrence Crowell

It is certainly not impossible that our observable universe is a simulation. It could be that in some other cosmology that mass-energy is not dispersed nearly as far as in our world and that IGUS beings are then simulating our world. However, inflationary cosmology does indicate that mass-energy is highly diffuse in cosmologies and the limit of light speed prevents beings from accumulating enough mass-energy to simulate the 10^{100}qubits of information necessary to generate our universe. Even a highly partial universe would require a vast amount of mass-energy to construct the information we observe locally. It is not absolutely impossible, but I think it is not highly probable.

These ideas do have some cross currents with religion. What if God is just a super-user in another cosmology? It reminds me of the 90s song, "What if God is a slob like one of us?" Of course God in the proper theological sense would be an infinite super-user, and infinity has a funny way of making analysis less tractable.

Religions are in a way a map of the human psyche. Look at the description of the sanctuary in Leviticus with the outer court, inner compartment and the Holy of Holies. This is a mirror of the Freudian idea of Id, Ego and Superego. Our beliefs about God, or gods, are in many ways representations of ourselves.

James Dunn

If we are living in a construct that allows for simulation, then we ourselves may be able to use the underlying construct in Building Universes - Relativity from Quantum Causality.

http://vixra.org/pdf/1402.0041v1.pdf

Is this what you are referring to?

James Dunn

Re: 3 Implications for intelligent life

So if you have a computer model, where there is environment evolved consciousness. Your statements seem to imply that a lack of substantive structure is an indication of a simulated environment. This is the realm of present particle physics, there is nothing substantive below the size of an atom. Yet artifact considered as subatomic particles have features larger than an atom; like boson. This contradiction seems to be supported by as yet non-observable systems of causal connectedness.

"Connectedness" is not a proper word. But it is a key feature in describing causality that exists despite and without direct reference to energy.

Energy has a component of m/s or space/time. As long as Qubits are related directly to space/time then energy is a required consideration. However, as in quantum entanglement, energy need not be a consideration related to a logic state. We may yet not have the means of creating an energy-less evolving causal state, but that does not mean it is not possible.

No two things can occupy the same space at the same time; in macro-physics. but in subatomic physics many things occupy the same space at the same time. There is no empty space anywhere in a Universe of Relativity.

Illusion is simply any system that is considered with incompletely considered perspectives. Everything we know is incomplete, so yes, cosmology from our perspectives is an illusion.

Probability, error tolerance, and limitations for approximations mask causality.

The contradiction between the macro and subatomic worlds seems to indicate a structural component of causality. Many more than one set of connectedness can share a causal component. The simple (exaggeration) shift of a causal connection is like the difference in spin observed in quantum entanglement. Seemingly instantaneous propagation. But outside of relativity, it is potentially just a slight shift between similar causal systems; energy-less.

The potential is that Building Universes - Relativity from Quantum Causality can be done without any energy at all except where we want to interface our space/time tools with the universes we build.

The universes we build need not have the same physics constants as our universe. As such, we can build alternate dimensional spaces. When interfaced with our universe; warping of space/time, worm holes, black holes, gateways between locations, quantum cameras ...

James Dunn

I believe we can build a mechanism to Exactly model our universe, and manipulate it to create computational systems. But the physical outcomes will exactly match physics and not the approximations provided by mathematics.

In any "real" physical environment, it would take an extraordinary number of seemingly abstract mathematics relationships to model the systems of relationships that are in constant change within a cubic centimeter. To do so without error is presently and for the foreseeable future impossible.

However, by using the structure of the universe to build a system for analyzing a piece within our universe (quantum camera), then we are not relying upon approximations. Math will likely still be used, to get us into the general area we want to be. But the quantum camera would respond and interact with the our universe exactly.

The quantum camera would be a subset of a universe that we build.

James Dunn

To be sure, this is not pie in the sky relationships.

Billions of dollars in grants are available for this type of research:

https://www.fbo.gov/index?s=opportunity&mode=form&id=7fa50ea731f2aa4529b223b7f5b38987&tab=core&_cview=1

But who will control the technologies developed?

Business Model to Broadly teach Common Sense:

How should we steer the future of humanity?

http://fqxi.org/community/forum/topic/2045

Method for ethically monitoring and eliminating all corrruption:

Corruption = unethical allocation of resources and/or opportunities

http://eliminate-all-corruption.pbworks.com

Eliminating corruption from both the Top/Down (management of NSA) AND Bottom/Up (broadly teaching Common Sense).

Lawrence Crowell

James,

In response to the first couple of posts ... A computer simulation does not come for free. One has to access enough mass-energy to assemble the bits of information necessary. The Khinchin-Shannon information of an information bit with probability P_n is I_n = log_2(P_n), and the entropy of a string of these information bits is

S = -k sum_nP_n I_n = -k sum_n P_n log_2(P_n).

Entropy is energy per temperature and the energy associated with it is E = TS. So beings must access a huge amount of energy to simulate a world completely. Even we lowly humans have to plug our Xbox360s or PS3s into the wall in order to run our world simulations or games. A complete simulation of Earth on and near the surface with avatars plugged into the "game" would require a vast amount of energy to run. Simulations of every larger scales explodes the amount of energy required, which translates into using machines that transform available bits or qubits in the world into those which construct the simulation.

Cheers LC

James Dunn

I am not very familiar with Khinchin-Shannon. Isn't that Information Theory based in probability?

Probability, Limits, and Error Analysis hide systems of causality to simplify analysis; i.e. approximations.

Probability depends upon Relativity; Relativity does not depend upon Probability. Probability enforces space/time considerations in the form of things that are observable. Probability washes out orders of magnitudes of complexities regarding secondary/tertiary/... systems of causality. Probability is based in reinforcing approximations to increasing degrees of exactness related to observable outcomes of physics; but ignores causal relationships buried by probability. These causal relationships are the basis of Axiom of Choice, not probability.

I am not saying that probability is without use; but it is not a final solution.

Consider two adjacent (simplification) photon of two different energies that has departed from a galaxy billions of light-years from Earth. They arrived adjacent and with measurable energies. What should the energies be with squared of the distance losses? What should the energies be based on billions of years of entropy? How many varying densities of hydrogen atom distributions were in close proximity to the photons over the billions of light-years of travel (wavelet distortions)? Combine these and the photons arrive with significantly stronger energies and without distortions from passing through gravity distortions.

What else unrelated directly to energy is going on, and how can we use it?

Just my opinions,

I will look up Khinchin-Shannon and see what they have to say.

Georgina Woodward

Lawrence,

you have written a really interesting essay. I didn't expect to enjoy it but I really did. I didn't understand the middle section of course.

Virtual or real extinction what's the difference? Unless there is some way to hack the simulation and make the environmental issues go away...You seem to be saying that the universe can not be simulated (and so that's not going to work.)

We need to be very cautious about geo-engineering because we don't want to make things accidentally worse. The examples of hydroelectric dam problems, silting, damaging fisheries, affecting water supply, preventing nutrients fertilizing land down river; and the problems of 'green'palm oil production fueling deforestation and orangutan habitat destruction should be cautionary tales. Both were solutions!

The many worlds idea kind of blurs the issues. We need to concentrate on the infrastructure and planning we need to get to the next century and beyond in this world. I agree we are not ready yet for space but I have suggested that perhaps learning to survive on a hostile Earth could be preparation for colonization of other worlds later on.

Thank you a good read. Best of luck, Georgina

Lawrence Crowell

The main thesis of my essay is not concerned with the eternal survival of the human race. The point is that it is not likely there can exist an intelligent system or set of beings in the universe that can completely simulate a cosmology to the level of detail we observe. The point is that the probability our universe is an objective universe, not the creation by some beings elsewhere with galactic sized deep-thought computers, is reasonably close to unity.

The survival of our species is likely to be more and more contingent upon our decisions. We may be forced into some forms of geo-engineering, whether we want it or not. It is a dicey proposition, and it could have pitfalls. However, recent data indicates that the methane trigger has gone off with hydrate and permafrost melt. Trying to reduce global warming by just reducing CO_2 output appears to be a case of closing the barn door after the horses have escaped.

Cheers LC

Georgina Woodward

Just a thought; Aren't we 'simulating' it, piece by piece, when we collect the data and form it into images of the cosmos? The visible universe is not the material, (made of atoms and fermion particles), universe that exists out in space, IMHO.

I am becoming more and more amazed by how very complex things can be formed by simple reiteration of algorithms. Just looking at fractals we can see details within details, within details,and so on, but simply produced. Which could possibly undermine the premise that it takes huge computing power to produce something dreadfully complex. Building unimaginable shapes,Michael Hansmeyer Those shapes are amazing!

Not that I'm saying the cosmos is a computer simulation, but thinking about how you came to that conclusion.

Christian Corda

Hi LC,

My entry has been just put online, see Bohr-like model for black holes: the route for quantum gravity.

I am going to carefully read, comment and score your entry.

Cheers,

Ch.

Christian Corda

Dear LC,

I enjoyed a lot in reading your beautiful and well written Essay. Here are some comments:

1) Let us consider your statement that "a black hole is the smallest region in which information can be contained". As the gravitational radius of the universe is of the same order of the Hubble radius, the universe should be the smallest region in which all information of the universe can be contained. This endorses your statements that "The only "computer" capable of simulating the universe is the universe itself" and that "it is not possible for humans or any intelligent life to completely simulate the universe." On the other hand, considering a "multiverse prospective", holographic principle implies that all the information in our universe should be contained in the universe event horizon, which is of order of the Hubble sphere. Thus, it could be, in principle, possible, for an "external" observers (type V collective) to access to the information in our universe and, in turn, to simulate our universe. Fortunately, causality of relativity and nonlocality and non-signaling in quantum mechanics prevent this possibility. In my opinion, this implies that causality of relativity and nonlocality and non-signaling in quantum mechanics are, in a certain sense, foundations of the anthropic principle.

2) I find tremendous,but correct, your observation that "Given the rate of economic and energy growth of the human race faster than light travel implies we will consume the entire observable universe in the next few million years."

3) It is correct my understanding that you balance your pessimistic tapestry with the emerging of the anthropic principle?

Cheers, Ch.

Lawrence Crowell

Christian,

I have been a bit slow in getting to many essays. Frankly most of them are a bit on the prosaic side. The question involves the question of whether humanity can plan a course of action which insures our survival into the future. As a result many essays are "blueprints" for our actions, which are by implication suggestions for either policy objectives or highly fantastical futurist ideas. I find it a bit much to assume these things can take shape the way any writer might suppose. I am certainly the last person to think a future course that optimizes our condition and survival can be derived by me. At best I think that maybe a sort of global democratic forum might in the long run be the better format for this.

My essay is in some ways a way of discussing some quantum cosmological implications. My take on the future of humanity is that we are probably not eternal, at least without some divine eschatological input that lies outside the domain of science, and that our survival is then contingent. This then connects with what possible limits there are to the power of IGUS (information gathering & utilizing systems) beings which has certain cosmological bases. These limits are based upon a horizon structure of the universe and the global property of the speed of light as a projective quantity that intertwines ruler and clock measurements. This is as you say a sort of revision of the anthropic principle, which is something I am happy with when it comes to the weak AP. The strong AP is suspicious in my opinion.

The cosmological duality that I think is the most salient in line with this is the duality between the Planck/string length and the cosmological particle horizon length. The Planck scale is the smallest region in which one can isolate a quantum bit with near unit probability. On a scale smaller it is simply impossible to isolate a qubit with unit probability. The particle horizon is the largest scale in which one can determine the diffeomorphism structure of spacetime, or in other words establish an arrow of time. The quantum bit when multiplied by k gives entropy measure of information, and the temperature assigns the energy equivalent to this. This is a quantum complement set of observables and their scale limit. The scale limit is determined by dual horizons, the absolute horizon scale of Planck and the relative horizon in any region of the observable universe.

I argue along lines similar to Raamsdonk that space and time are manifestations of entanglements. In fact I think general relativity and quantum mechanics are different manifestations of the same thing. The ADM Hamiltonian constraint equation is NH = 0 which in the quantum sense is NОЁ[g] = 0. This departs from the Schroedinger equation because there is no -iв€‚ОЁ[g]/в€‚t term. There is then no global Killing vector of the sort K_t = в€‚_t. However, local observers measure time according to a clock. So a local observer in region A measures time, but this may be different from region B. The Hamiltonian for this system is for independent states then H = H_aвЉ--I вЉ• IвЉ--H_b so that a time dependent |П€_a(t)> may be found by projecting onto the total state vector |ОЁ[g]> with the local vector

Lawrence Crowell

This does not like reverse carrot signs

\langle ψ_b|. This means that time is a subjective quantity just as any state vector or wave is.

In Misner, Thorne and Wheeler "Gravitation" with Ch21 there is the discussion of the "many fingered time," which points to how the analyst or observer can push time into the future according to any procedure. Time is in effect chosen by the analyst-observer and not something "given" by nature. I think in some fashion this is what connects quantum mechanics and general relativity, in fact implies an equivalency between the two.

Cosmological examples of this are the de Sitter and anti-de Sitter spacetimes. The metric equations are not globally extendible on the entire manifold, but exist only on certain coordinate patches. There are then no global coordinate systems, and by extension no global meaning to time. In the eternal inflationary scenario regions of the manifold quantum tunnel into a different vacuum state and define disconnected manifolds as pockets or bubbles. These then have their separate time direction with no extension to the dS manifold of inflation. A similar case may be argued for the AdS manifold as well.

Cheers LC

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