NMT (No-Me Teaching) new series 32:
Fine-Tuned Universe 23:
There is a simple argument that if the BB problem exists for the random fluctuation multiverse, then the same problem exists for the inflationary multiverse. Define a megaverse as some very large finite, or even infinite, region of space-time of a universe or multiverse that has some configuration of mass-energy in it. [We use the idea of a megaverse to avoid problems arising from defining a measure if the multiverse is infinite. If the multiverse is infinite, we could avoid such potential problems by making our megaverse finite but large enough to include many observers.] The BB problem arises for a random fluctuation multiverse because, when the standard measure M of statistical mechanics is applied to the phase space of an arbitrary megaverse, the measure of configurations dominated by non-BB observers is much, much smaller than that of those configurations dominated by BB observers. Further, if this is true for the entire megaverse, then it will have to be true for any arbitrarily chosen spacelike hypersurface, hp, of constant time t of the megaverse. Thus, if we let Mt(BB) designate the measure of volume, Vt(BB), of the phase space of hp corresponding to those configurations dominated by BB observers, and Mt(~BB) designate the measure of the volume, Vt(~BB), of hp corresponding to configurations dominated by non-BB observers, then Mt(~BB)/Mt(BB) << 1. [A universe is dominated by non-BB (~BB) observers if and only if it contains at least one observer, and in some well-defined sense there is a greater proportion of non-BB observers than BB observers.] That is, the measure for the possible mass-energy-momentum configurations of hp that are non-BB dominated will be much, much smaller than the measure for those configurations that are BB dominated. Assuming that the laws of physics are deterministic and time-reversal invariant, then the measure is time-invariant, as explained in Section 2.4. If we consider the mass-energy-momentum configurations of hp as evolving with time, this means that for any volume of phase space V(t0) of measure MV(t0) at time t0, V(t0) will evolve into a volume V(t) of the same measure at time t: that is, MV(t) = MV(t0).
Now, consider the initial conditions of the megaverse defined on some spacelike hypersurface of constant time t0. Let Vt0(BB) and Vt0(~BB) represent the volume of phase space of that hypersurface that evolves into configurations dominated by BB observers and by non- BB observers, respectively, for some later hypersurface at time t. Since the statistical mechanics measure m is time-invariant, the ratio of the measure of Vt0(~BB) to Vt0(BB), that is, Mt0(~BB)/Mt0(BB), will remain the same. Consequently, Mt0(~BB)/Mt0(BB) = Mt(~BB)/ Mt(BB) << 1. This means that the measure of initial states that give rise to a universe dominated by non-BB observers at some arbitrarily chosen later time t is much, much smaller than the measure of initial states that give rise to a universe dominated by BB observers at t. Consequently, unless the initial state of the megaverse is in a very special low-probability state – that corresponding to volume Vt0(~BB) – it will not give rise to a universe dominated by non-BBs. This is true for any megaverse in which the laws of physics are deterministic and time-reversal invariant. Inflationary cosmology denies neither of these assumptions. Further, even though the laws of physics are not strictly speaking time-reversal invariant – since timereversal symmetry is broken in weak interactions, notably the decay of neutral kaons – the argument offered by Albrecht and others that was explicated in Section 6.3.3 does not, in any way, exploit this lack of invariance, nor does it exploit any sort of quantum indeterminacy. Thus, without assuming highly special initial conditions, inflationary cosmology cannot do better with regard to the BB problem than the random fluctuation Multi-Verse.
To illustrate this argument, consider the following analogy. Let a highly ordered, lowentropy non-BB-dominated megaverse of finite volume containing observers be represented as a black-and-white TV screen with rows and rows of O’s throughout, and let a megaverse dominated by BBs be represented by occasional O’s with large patches of “snow” – that is, “random” configurations of black-and-white pixels. We shall call the former arrangement the ordered, non-BB-pixel arrangement, and the latter the BB-pixel arrangement. For simplicity, suppose there are only a finite number of pixels on the TV screen. In that case, the number of ordered non-BB-pixel arrangements would be very small compared with BB-pixel arrangements. Further, suppose the image on the TV screen is being generated by some small magnetic patch on a videocassette recorder (VCR) tape that the VCR head is reading. Finally, suppose that there is a one-to-one correspondence between arrangements of magnetic particles on the patch and the possible configurations of black and- white pixels on the screen.
Because of the one-to-one correspondence, the ratio of possible configurations of magnetic particles on the patch of tape that give rise to non-BB-pixel arrangements to those that give rise to BB arrangements will be the same as the ratio of non-BB-pixel arrangements to BB-pixel arrangements on the TV screen. Thus, if the latter ratio is enormously small, so will the former ratio. This is analogous to what happens in the inflationary megaverse: because the laws of physics are deterministic and time-reversal invariant, every microstate m(t0) at time t0 evolves into one and only one microstate, m(t), at time t, and, hence, they can be put into a one-to-one correspondence. Consequently, just as the ratios of the number of non-BB-pixel configurations to the BB-pixel configurations is preserved from VCR patch to TV screen, the ratio of the measure of initial configurations that lead to non-BB-dominant universes to the measure of those that lead to BB-dominant universes is the same as the corresponding ratio at a later time t.
[The fundamental error in Albrecht’s reasoning can be illustrated by another analogy. Consider a balloon that is being unevenly inflated. Suppose some patches of its two-dimensional surface are massively blown up – say by a trillionfold in each of its two dimensions (e.g. one-trillionth of a meter becomes a meter). This corresponds to the space out of which bubble universes form, some parts of which are inflated and other parts of which are not. Now, suppose one of the blown-up patches is one square meter in volume and is completely covered by adjacent black Os that are one centimeter in diameter, with the space in between simply consisting of random mix of black-and-white dots. The scale of the order on this patch is one centimeter; at a level of less than one centimeter, there is a random mix of black-and-white dots. The crucial thing to note, however, is that scale of order of the pre-blown-up patch will be much, much smaller: one-trillionth of a centimeter. Now it is true that for any two patches, larger patches of the same order and scale of order will be much less likely to occur at random than small patches with the same order and scale – for example, a patch covered with adjacent Os of 1 cm in diameter that has an area of one square meter is much more likely to occur at random than a patch covered with the same pattern of Os that has an area of a thousand square meters. This kind of consideration misleads Albrecht into thinking that very small patches of space-time that inflate into large observer filled, non-BB dominated universes are vastly more likely to occur than large patches of space-time that form a non-BB-observer-filled universe via a thermal fluctuation. Consequently, Albrecht is misled into thinking that inflation can help overcome the BB problem confronting the RF model by increasing the relative proportion of non-BB observers. The problem for Albrecht’s reasoning is that in order to produce a non-BB observer-dominant universe, the order of the patch that inflates would have to be at a vastly smaller scale – for example, inversely proportional to the factor by which the patch inflated– and hence contain a vastly higher degree of order per unit of volume than a corresponding non-BB-observer patch of the size of our universe that did not inflate. The decrease in likelihood resulting from the higher degree of order compensates for the increase in probability resulting from the size of the patch, as can be seen by our more rigorous argument offered earlier based on the time-invariance of the standard measure. In terms of our balloon analogy, a square patch with sides one-trillionth of a meter in length filled with adjacent Os one-trillionth of a centimeter in diameter is no more likely to occur at random than a square patch with sides of 1 m in length filled with Os that are 1 cm in diameter.]
Some might try to dispute one or more of the assumptions of this argument. The most vulnerable assumptions are the problems of non-arbitrarily dealing with the possible infinities that might arise when one attempts to define a measure for the entire megaverse, along with the additional problem of making rigorous the claim that in the entire phase space, the measure of non-BB-dominated hypersurfaces is much, much less than that of BB-dominated hypersurfaces. These problems, however, are as much a problem for making Albrecht’s argument rigorous. The whole point of Albrecht’s argument is that inflation does better with regard to BBs than the random fluctuation multiverse. In order for this claim to be true, there must be some “correct” measure M for the possible mass-energy states of the multiverse (or at least for arbitrarily chosen very large finite subsets of it) such that non-BB-observer-dominated states have a much, much smaller measure than those of BB-observer-dominated states for the random fluctuation model.
In response, perhaps Albrecht could appeal to some notion of a “generic” initial state that is not dependent on the existence of a measure over phase space. Such an appeal, however, will immediately run afoul an objection Penrose has raised. Consider an enormously large universe that eventually collapses back on itself and assume that all the special laws that are required by inflation hold in that universe. (We could even have an infinite universe with a negative cosmological constant to ensure collapse.) Suppose that this universe had many domains, some of which are highly irregular. In fact, we can suppose that it is chock full of BBs. As Penrose points out, the collapse of such a universe will result in “a generic space-time singularity, as we can reasonably infer from precise mathematical theorems” (2004, p. 756). Assuming that the laws of physics (including those of inflation) are time-symmetric (as is typically assumed in these contexts), if we now reverse the direction of time in our model, we shall “obtain an evolution which starts from a general-looking singularity and then becomes whatever irregular type of universe we may care to choose” (2004, p. 757). Since the laws governing inflation will hold in this time-reversed situation, it follows that one cannot guarantee that a uniform or non-BB-dominant universe will arise from generic initial conditions. Thus, inflationary cosmology can explain such a universe only by effectively presupposing those subsets of generic initial conditions that will lead this type of universe. As Penrose notes, “The point is that whether or not we actually have inflation, the physical possibility of an inflationary period is of no use whatever in attempts to ensure that evolution from a generic singularity will lead to a uniform (or spatially flat) universe” .
The above arguments do not show that inflationary cosmology is wrong or even that scientists are unjustified in accepting it. What they do show is that the inflationary multiverse offers no help in eliminating either the fine-tuning of the laws of nature or the special low-entropic initial conditions of the big bang. With regard to the special low-entropic initial conditions, it can explain the special conditions of the big bang only by hypothesizing some other, even more special, set of initial conditions. Although a chaotic inflationary model might lead one to expect a universe like ours, unless highly special initial conditions are assumed across the entire multiverse, it leads to a multiverse dominated by BBs for all later times and thus does no better than a random fluctuation model. It also runs into the generic problems faced by multiverse hypotheses. If we find the existence of a BB dominated multiverses unacceptable, it follows that an inflationary-superstring multiverse at best eliminates only the need to explain the life-permitting values of the constants of physics (and perhaps other non-entropic types of special initial conditions). Because of the highly speculative extra laws and conditions required to make an inflationary multiverse work, one could not be blamed if one judged that such purported explanatory ability were far too costly.
Some more selected verses from the Ramana Maharshi disciple, Master Nome disciple:
Those who would know the Self by Knowledge, cease to regard the Senses as a measure of Reality or of the Self. Non-sensory Knowledge reveals the Self’s freedom from the Senses & sets one free of the limitations of the Senses. Those who know that there is neither permanence of the Senses, nor Happiness via the Senses, who do not equate Pleasure with Happiness, of equate Pain with Suffering, but realize that Happiness & Suffering are determined by Knowledge of the Self or Ignorance respectively. Those who desire to experience the spiritual Truth beyond the Senses, take recourse to the Inquiry to know the Self. By such Inquiry, the Knowledge, that the Self is innately transcendent of the Senses & not bound by the Senses in any manner, shines. The Knowledge of the Self is itself free from limitations of the Senses, as is the Self itself. Those who abide in this Knowledge remain unmoved by whatever happens to the Senses. By Knowledge of the Self, Knowledge of Reality, one brings about the destruction of the foundations of the delusion of believing in the existence of an external World.
The Wise know that the Senses do not & cannot provide Happiness, that Attachment to the Senses or their objects, is Bondage. They know that the Senses are neither Bliss nor Immortal. They know that the Purpose of Life is not fulfilled by any kind of sensory experience. They know that Liberation is not any kind of sensory experience & that Realization is not a particular kind of Sensation. Realization is not an increase in Sensation & not an decrease in Sensation. One’s freedom from the Senses must be firm & natural for there to be Realization. This necessitates the Knowledge of the Self’s transcendence of the Senses. The Self is Infinite Consciousness, unchanging Existence, perfectly full Bliss. Vast & space-like, formless & unconditioned is the Self. Of immense, silent Peace, ever-shining & motionless, is the Self. Within the Self, without actually occurring, there is imagined the "real" of objective experience, manifesting as the World perceived by the 5 Senses. Those 5 Senses so appear, unreal but imagined, with their corresponding sense-objects (sights, sounds, feelings, odors, tastes). Within the different realms of the different Senses, a great variety of sensations & an apparently uncountable number or sense objects appear.
These are the Sense experiences of living beings, which are differentiated from one another by means of Mis-identification with the Body. Like the surface ripples & foam on the waves in the
, like clouds in the Sky of pure Being, so are
the Senses. The Self is Existence-Consciousness-Happiness. To confound the Self
with any or all of the Senses, in any way, is Ignorance. Freedom from Mis-identification
with the Senses is Knowledge. Since Knowledge is Liberation, & since one
seeks to know Reality & not create it, for Reality always is, therefore,
one should discern clearly the Self. The Self is innately free from the Senses,
& the Self is free from all the limitations of the Senses. The Self is
singular & indivisible Existence. Sea of
The Senses are multiple & divided. The Senses are changeful, discontinuous, & impermanent. The Senses are lost (for some eventually or accidentally), dulled, or altered in death, old age, & illness. The Senses change during one’s Lifetime, from infancy until the end of the Body. The Senses are changing all the time, transforming into dull & acute states, subject as they are to the 3 gunas – the “qualities” of tamas (inertia), rajas (agitation), sattva (tending toward the light of Knowledge). Each of the 5 Senses takes a turn due to a change of the Sense Organ, the mental attention, & similar factors. The Senses appear only in the Waking state. With each state of Mind (Waking, Dream, Deep Dreamless Sleep), the Senses change. Upon death of the Body, which is not the Self, the Senses are lost entirely. Rarely are all the 5 Senses active or experienced, simultaneously, but Existence is always wholly present. The Senses are just a momentary function.
The Self, however, is steady, self-existent Reality, permanent & not a function of some other thing. The Self is Being & not a doing or activity. The Self is not determined by any conditions & is itself without any conditions whatsoever. The Senses, though, are determined by any current conditions such as the condition of the Sense Organs & the environment. The experience of these is determined as the result of the interaction of what appears to have become split in Consciousness – that the object & the instrument (Sense Organ) used to know it – & the mental attention given to or removed from the Senses. From a higher view, in the one Mind, all 3 changing factors (object, instrument, mental attention) appear, determining the 5 Sense experiences. Partless Existence, which is the Self, is beyond the changeful appearances in the Mind. So, how can the Senses be considered to be the Self ?
The above themes & 1600 pages more are freely available as perused or downloaded PDF’s, the sole occupants of a Public Microsoft Skydrive “Public Folder” accessible through:
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