a.v. yurov and v.a. yurov- one more observational consequence of many-worlds quantum theory

8/3/2019 A.V. Yurov and V.A. Yurov- One more observational consequence of many-worlds quantum theory

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Then we appears to be merely prisoners in cosmicprison of a radius R = c/H, where Hubble constant

H =

8G

/3. After 1017 yr each and every star inthe universe will be either black hole, black dwarf or neu-tron star; 1010 Gyr later the temperature of neutron starswill decrease to less than 100 K. It is mildly speakingunlikely that human-observers will be able to endure insuch inhospitable universe. However, it wouldnt really

matter at that point, because no life (including human-observers) will be able to exist there forever due to bothproton decay (its time life tpr > 10

32 yr) and the ex-ponential falloff of the density of matter (information,being processed in ever-expanding universes was consid-ered in [8]. There has been shown that an infinite amountof information can be processed via the usage of tem-perature gradients created by gravitational tidal energy,but only in assumption that the cosmological constant isequally zero). Therefore if tf googleplex then exceptfor unimaginably tiny initial period from the big bang totpr the universe will be absolutely dead. It is definitelynot bright future at all!

On the other hand, taking into account the unimag-inably long lifetime of such universe we shall concludethat all possible events, including those with extremelylow probability, will someday occur. One of the mostinteresting of those unlikely events would be the spon-taneous appearance from quantum fluctuations of ob-servers, surrounded by environment suitable to per-mit the observation. With this conclusion, it wouldbe only natural to ask: can we in principle be one ofthose vacuum observers? And, more generally: un-der what circumstances will the ordered (i.e. classical)observations dominate over vacuum ones? Page givesthe following answer: if t < tmax = 1060 yr, and onlythen will the human observations be with high probail-

ity ordered. Otherwise, almost all observations in theuniverse will have its root in vacuum fluctuations. Asthe result, in universe with tmax tf googleplex our,obviously ordered, observations are to be considered assomething embarassingly atypical. Page concludes that This extreme atypicality is like an extremely low like-lihood, counting as very strong observational evidenceagainst any theory predicting such a long-lived universewith a quantum state that can allow localized observa-tions, and makes the prediction that the universe just

will not last long enough to give 4-volume > e1050

.To show this in work, lets consider the total 4-volume

of universe:

V4(t) = c

t0

dta3(t). (1)

The probability of vacuum fluctuations pvac < pbrwhereas the probability of ordered occurrences pord >

pbr. Multiplying V4(t) by pord results in the volume ofthe part of total V4(t) where ordered occurrences aredominating ones. Now let N be the number of observa-tions, made during the past human history. The productN V4(br) will mark the part of total V4(t) where ordered

human observations all take place. If humans are the typ-ical observers (anthropic principle!) then one can expectthat

V4(t)pord V4(br)N. (2)

Substituting a(t) = a0eHt into the (1) one get V4(t). Fol-lowing Page we can evaluate N e48. Substituting Nand V4(t) into the (2) allows us to express pord. Finally,using the inequality pord > pbr one comes to conclusionthat, under those circumstances, the timelife of the dSuniverse is indeed t < tmax = 10

60 yr.

III. PHANTOM ENERGY

Lets see, what will happen with Page results in theuniverse filled with phantom energy. It appears, that incontrast to dS models, for such universes we get a re-markable concordance: tf = tmax up to very high degreeof accuracy.

Before we start, we should mention, that the partic-

ular interest to the models with phantom fields arisesfrom their prediction of so-called Cosmic Doomsdayalias big rip [9]. Since for the phantom energy we havew = p/(c2) = 1 with > 0, the integration of theEinstein-Friedmann equations for the flat universe resultsin

a(t) =a0

(1 t)2/3,

(t) = 0

a(t)

a0

3=

0(1 t)2 ,

(3)

where =

6G0. Choosing t = 0 as the present time,

a0 1028

cm and 0 = 1.4c/( 2 + 3) as the present val-ues of the scale factor and the density (If 1 then0 0.7 1029 g/cm3), at time t = tf = 1/, we auto-matically get the big rip.

Now, lets return to our question. Equations (1) and(3), taken together, lead to

V4(t) =ca30

(2 )

1

(1 t/tf)(2)/ 1

+ V4(0),

where V4(0) = a40 = 10112 cm4 = e258 cm4. Using Page

approach we have

ca

3

0(2 )

1(1 t/tf)(2)/

1 < V4(br)eSbr/ V4(0).The second member of the equation is

3 e48 1012 e1050 e258 e1050,

therefore 1 t

tf

(2)/< e10

50

. (4)


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TABLE I:

tf yr tmax/tf

2.3 1059 0.91.1 1059 0.997.7 1058 0.9995.8 1058 0.99994.6 1058 0.99999

In the case 1 we get

tf ttf

> exp

0.5 10

50

tf

6G0

= exp

1.685 10

67

tf

.

(5)Now, we have to consider 3 different cases.

a. tf 1.685 1067 s = 5.3 1059 yr. In thiscase the power of exponent in (5) is small enough to usethe expansion in Taylors series. Its application results

in inequality t < tmax = 5.3 1059

yr. This leaves uswith the same problem as in dS situation: the end of theworld will take place at t = tf but ordered observationwill be dominating ones while t tf only.

b. tf 1.685 1067 s. In this case

t < tmax = tf

1 e1.6851067/tf

tf.

Here we come to remarkable difference between phantomand dS cosmologies. While in the last case we havetmax = 10

60 yr

tf > googleplex, where tmax follows

from Pages reasoning and tf is the string theoryprediction, in the former case the situation can be muchmore agreeable: in fact, the validity of the b conditionensures that tmax tf. As we can see from Tabl. I,tmax tf very fast when tf decreases. Iftf = 5.31050yr then tmax = tf(1 e10

9

) and tf = 22 Gyr stands

for tmax = tf(1 e1050

), thus actually erasing the verydifference between tmax and tf.

c. tf 1.685 1067 s. This case implies

tmax = 11

e tf 0.63tf.

Therefore, in such Universe only about half of all ob-servers can assuredly consider themselves classical andhaving the naturally ordered observations, which is suffi-ciently better then what we had in dS universe, yet stillbeing far from perfect.

Summarizing all of the above, we can conclude that theone and essentially the only convenient case is b. Afterall, for tf < 10

59 yr it gives us tf tmax for granted!

IV. THE NUMBER OF COARSE-GRAINED

HISTORIES

For the time being, the physical meaning of phantomfields is as yet unclear. For this reason lets return backto the realistic case of dS universe and seeming inconsis-tency between tmax and tf (tmax tf), that has beenfound in it. The core of Pages argumentation is the

equation (2). But lets inspect carefully the quantities,forming it. It is clear that, by complete analogy with pbr,quantity pord should be calculated by quantum laws. In-deed, in the framework of Page approach one need makea comparison pbr with pord. It is as well to remember that

pbr is the quantum quantity, therefore, generally speak-ing, the same must be true for the pord. As a matter offact, pord = eSord/. Therefore, l.h.s of equation (2) isdependant on . But the equivalence will hold only ifthe same will be true for the r.h.s.! If the value V4(br) ispurely classical, then N is the only remaining candidatefor the dependancy on .

At a first glance this conclusion seems absolutely

grotesque, but it appears to be right in touch with Pageresonings. As a matter of fact, in his article Page dealswith quantum (or semi-classical) observers. The numberof quantum observers N is the quantum quantity andhence, must be calculated by the quantum laws. Fromthis point of view, it is no wonder that N will depend on.

But if this is correct, then one cant use Page estimate(N e48) anymore. Unfortunately, we cant calculateN explicitly, but we can evaluate it upon usage of verysimple quantum-based reasoning. It is already clear thatnew N should be much greater then e48. As we shallsee, this number can exceed even gogleplex, thus totallyrefuting Page argument.

One can roughly evaluate the number N as the numberof coarse-grained histories: N = Nh = N

Ncb where Nc is

the number of spacetime cells and Nb is the number ofrelevant bins in field space. In the article [10] Garriga andVilenkin have made this for the spacetime volume withthe size R = ct0 where t0 = 1010 yr. As a result they got

N e10244. Substituting this value into the (2) one gettmax = 10261 yr. This number is by many orders greaterthan Pages 1060 yr but is still too small in comparison

with e10131

. However, the number N easily allows foradditional incease up to to the point, where tmax will becomparable with strings predictions.

Indeed, remaining in framework of quantum theory we

should consider all possible observers, including thosewho are living in much older universes where vacuumenergy already exceeds the total density of all the otherenergy components in the universe. In such universes

V4(t) ca30

24G

e

24G = e0.510

17t.

For example, if t = 1017 yr (the era of black holes) one

have V4 = e0.2108 and if t = 1032 yr (the low bound


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4

of proton lifetime) then V4 = e0.21023. The number of

spacetime cells of size L will be Nc V4(t)/L4 e108

in first case and Nc e1023

in the second one. But inall cases the values of N are given by supergoogleplexnumbers:

N = ee108

, N = ee1023

.

Substituting them in (2) we finally get tmax = e108

yr ortmax = e

1023 yr.The interesting fact here is that both these numbers

lies in remarkable agreement with the results of [6]. Inparticular, for the case of 3 D3-branes with some parame-

ters there have been obtained theoretical value tf e1019

(lifetime on the NS5-brane). Decays due to decompacti-

fication are much faster: tf e1017

. Those are results ofthe models with the single KS throat. Consideration of 2KS throats (such models are more interesting since theyresult in positive cosmological constant whereas the mod-els with single KS throat result in < 0) in case of KPV

instantons leads to such value as tf

e109

- very good

agreement with the previously obtained tmax = e108

.In the case of general position one can conclude that

tmax = 1017e10

17t yr,

where t is the maximal possible lifetime of human-observers. Thus, if tmax =goggleplex one get t = 10

117

yr while tmax = e10123 yr implies t = 10140 yr. Of course,

it can be difficult to imagine that 10117 yr later the uni-verse will be filled by human-observers. Besides, it canbe argued whether such observers fits into the set beingreviewed or not. But the answer is very simple: when-ever the probability of finding ourselves in such universehas the nonzero value, we have to take it into account.

Finally, we should answer the following question: arethose auxiliary observers real, or not, i.e. can we as-cribe all of them to some really existing Universes, or arethey nothing more then vacuum probabilities? Theanswer is: yes, they have to be real; otherwise, we are

facing the situation, where the 1010100

quantum objectsare required to explain the existence of e48 (real) objects.Here is the same Pages paradox, only in other form andaggravated by much worsen numbers!

V. CONCLUSIONS

As we have seen, the assumption that N is the to-tal number of quantum observers results in such lifetimeof universe which is comparable with strings predictions.This creates the very strong grounds for serious consider-ation of such strange possibility. After all, the quantumnature ofN seems to be absolutely inevitable in quantumcosmology.

Of course, such state of affairs is something highlyunusual in everyday quantum mechanics. It has al-ready become a common fact, that in laboratory research

with neutron interferometer the neutron passing througha beam splitter will split into two neutrons. But inlab we dont expect that the same will be true for us.Observers are classical objects ad definition.

However, in quantum cosmology this situation changesdrastically. Since we are nothing but the part of theuniverse we have no choice but to consider ourselves asquantum objects. Page has shown in [11] that quantum

cosmology can give observational consequences of many-worlds quantum theory. We think that our results can beconsider as one more observational evidence of validity ofmany-worlds quantum theory.

REFERENCES

[1] Don N. Page, The Lifetime of the Universe,hep-th/0510003.

[2] N. Goheer, M. Kleban, and L. Susskind, The Trou-

ble With De Sitter Space. J. High Energy Phys.07, 056 (2003), hep-th/0212209

[3] S. Kachru, R. Kallosh, A. Linde, S. P. Trivedi, DeSitter Vacua in String Theory. Phys.Rev. D68(2003) 046005, hep-th/0301240.

[4] S. Kachru, J. Pearson, and H. Verlinde, Brane/FluxAnnihilation And the String Dual Of a Non-Supersymmetric Field Theory. JHEP 06 (2002)021, hep-th/0112197.

[5] I. R. Klebanov and M. J. Strassler, SupergravityAnd a Confining Gauge Theory: Duality Cascadesand chiSB-resolution of Naked Singularities. JHEP08 (2000) 052, hep-th/0007191.

[6] A. R. Frey, M. Lippert, and B. Williams, The Fallof Stringy De Sitter. Phys. Rev. D68, 046008(2003), hep-th/0305018.

[7] A. D. Chernin, Cosmic Vacuum. PHYS-USP. 44(11), 2001, 1099-1118.

[8] J.D. Barrow and S. Hervik, Information Process-ing in Ever-expanding Universes. Phys.Lett. B566(2003) 1-7, gr-qc/0302076.

[9] R.R. Caldwell, M. Kamionkowski and N.N. Wein-

berg, Phantom Energy and the Cosmic Dooms-day. Phys. Rev. Lett. 91 (2003) 071301,astro-ph/0302506.

[10] J. Garriga and A. Vilenkin, Many Worlds in One.Phys.Rev. D64 (2001) 043511, gr-qc/0102010.

[11] Don N. Page, Observational Conse-quences of Many-Worlds Quantum Theory,quant-ph/9904004.
http://arxiv.org/abs/hep-th/0510003http://arxiv.org/abs/hep-th/0212209http://arxiv.org/abs/hep-th/0301240http://arxiv.org/abs/hep-th/0112197http://arxiv.org/abs/hep-th/0007191http://arxiv.org/abs/hep-th/0305018http://arxiv.org/abs/gr-qc/0302076http://arxiv.org/abs/astro-ph/0302506http://arxiv.org/abs/gr-qc/0102010http://arxiv.org/abs/quant-ph/9904004http://arxiv.org/abs/quant-ph/9904004http://arxiv.org/abs/gr-qc/0102010http://arxiv.org/abs/astro-ph/0302506http://arxiv.org/abs/gr-qc/0302076http://arxiv.org/abs/hep-th/0305018http://arxiv.org/abs/hep-th/0007191http://arxiv.org/abs/hep-th/0112197http://arxiv.org/abs/hep-th/0301240http://arxiv.org/abs/hep-th/0212209http://arxiv.org/abs/hep-th/0510003

a.v. yurov and v.a. yurov- one more observational consequence of many-worlds quantum theory

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