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Figure 02-11 shows recent astronomical observations, which tend to support the hypothesis.
The diagram on the left illustrates the WMAP measurement^{b} of the fluctuations in the CMBR temperature. The strongest fluctuations are just over half a degree across, which indicates that space is very large or infinite. In addition, the diagram on the right illustrates the measurements of matter density from WMAP and 2dF Galaxy Redshift Survey^{c}. They are consistent with uniform distribution of matter on large scales.
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## Figure 02-11 Universe, Flat & Uniform [view large image] |

These observational data support the inflation theory, which suggests that the universe underwent an exponential expansion at 10^{-35} sec after the Big Bang. The universe became so large that it looks flat within our event horizon, and in addition, the contents in the universe were mixed uniformly as witnessed by the CMBR.
Our universe with a size of about 10 This conclusion is derived from elementary probability and does not assume speculative modern physics, merely that space is infinite (or at least sufficiently large) in size and almost uniformly filled with matter, as observations indicate. In infinite space, even the most unlikely events must take place somewhere. | |

## Figure 02-12 Parallel Universes [view large image] |

- Followings is a more elaborated deduction with simple mathematics:
- The radius of the observable universe is taken to be 4x10
^{26}m. It is assumed that the matter in the universe consists of nucleons, which has a radius of about 2x10^{-13}m. - Therefore, the universe has roughly 10
^{118}partitions for the nucleons. - These partitions can be filled or unfilled according to the configuration of the universe. The total number of different arrangements is 2
^{10118}. - A box with a radius of 2
^{10118}x10^{26}m ~ 2^{10118}m would exhausts all the possibilities. It contains possibly all kinds of parallel universes. - Beyond that box, universes - including ours - must repeat. The identical parallel universe would be about 2
^{10118}m away as shown in Figure 02-12.

- More exotic types and weird properties of multiverses are highlighted in the followings:
- In quantum mechanics the superposition of quantum states suddenly "collapsed" into a definite quantum state when we make a measurement. For example, measurement of the spin state for a spinning particle would yield either 1 or 0; it would not be any value in between. Generalization of this concept to the macroscopic world suggests that one classical reality would gradually split into superpositions of many as shown in Figure 02-13b. Observation experiences one of the splitting sequences by a decoherent process, which mimics wave function collapse. The classical states (no weird happening such as in two different places at once) are observed because they are in the most robust states.
- The level 4 multiverse is even more outlandish. It is suggested that the universe we experience is just a simulation running on an advanced civilization's supercomputer (Figure 02-13c). Since advanced civilizations would develop essentially unlimited computing power (see Moore's Law, Figure 02-13d), some of those can run "ancestor simulations" to reconstruct the history of their forebears or other beings. There could be a huge number of such simulations producing a one-to-one relationship between
- According to Superstring theory, there can be 100
^{500}different vacua each one corresponds to a different universe. Our universe and contiguous regions of space is a bubble embedded in an even vaster but mostly empty volume. Other bubbles exist out there, disconnected from ours. They nucleate like raindrops in a cloud. During nucleation, each one may acquire different strength of the forces, and may emerge with different spatial and temporal dimensions. It all depends on the outcome of symmetry breaking. The anthropic principle dictates that we see the universe the way it is because if it were different we would not be here to observe it. (see more in Topic 15 - Elementary Particles)

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## Figure 02-13b Level 3 Quantum Worlds | This kind of scenario is referred to as Multiverse level 3. It may be realized in the multiverses of level 1 and 2. |

## Figure 02-13c MV Level 4 |
## Figure 02-13d Moore's Law [view large image] |
mathematical models and the kind of universes mentioned in level 1, 2, and 3. |

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## Figure 02-13e Anthropic Principle |

Anyway in this observable universe, there are several parameters which seem to be fine tuned into a particular value beyond or below which life is not possible (see Table 02-03 for some of these so called Goldilocks parameters). Such fine tuning is often used to support the argument that someone, e.g., a God is doing the adjustment so as to allow us to exist. The resonant level of C

in Figure 02-14 (a), in which the 7.3367 Mev is the energy released in the nuclear reaction that produces the C^{12} nuclei and is in here adopted as the ground state. Further study reveals that there is a range of energies that is capable of producing same amount of C^{12} for life as shown in Figure 02-14 (b). The range is even wider if the "enough amount" (for life to exist) is included into the deliberation, so there is no "fine tuning" for the C^{12} resonant level after all. As for the other Goldilocks parameters in Table 02-03, it is pointed out that the tuning is done one by one while keeping all the others constant. The real world may not be that simple, many of these parameters would depend on each | |

## Figure 02-14 Resonant Level in C |
other - varying one would change the others so that the conclusions in the table have to be revised in the future with a more advanced theory. |

Parameter | Value | More | Less |
---|---|---|---|

Ratio of the Electromagnetic and gravitational forces | 10^{36} |
OK | Stars become smaller and die earlier making evolution of life unlikely |

Proportion of Mass Released as Energy when H Fused into He | 0.007 | All hydrogen would be consumed during the Big Bang, stars would not exit. | Nuclear fusion is impossible |

Ratio of Actual to Critical Cosmic Density | ~ 0.3 | Universe collapsed long ago | Rapid expansion prevents stars to form |

Ratio of Break-up and Total Energy for Galactic Supercluster | 10^{-5} |
Universe would be dominated by black holes - life is impossible | Universe would be structureless - life is impossible |

# of Spatial Dimensions (D) | 3 | Unstable planetary orbits for D = 4 | Life would be impossible for D = 2 |

Cosmological Constant | ~ 0.7 | Rapid expansion prevents stars to form | OK |

- The correspondence between mathematics and physics has been a source of debate that goes as far back as Aristotle and Plato. According to the Aristotelian paradigm, physical reality is fundamental and mathematical language is merely a useful tool. The Platonic argument considers the mathematical structure to be the true reality and observers only perceive it imperfectly. Thus a fundamental asymmetry appears to be built into the very heart of reality - why is only one of the many mathematical structures singled out to describe our universe? It is suggested that complete mathematical symmetry holds: that all mathematical structures exist physically as well. Every mathematical structure corresponds to a parallel universe. As a consequence, each universe is
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## Figure 02-15a Aristotele and Plato [view large image] |
governed by its own fundamental laws of physics (see more in Topic 15 - Elementary Particles). In Figure 02-15a Aristotle points down to the reality on earth while Plato points up to multiverse. |

Max Tegmark is a physics professor at MIT. He openly admits in his 2014 book titled "Our Mathematical Universe, My Quest for the Ultimate Nature of Reality" that he is a regular physicist at day and a wacky theorist at night. Currently (in 2014) his pet theory is (not surprisingly) mathematical universe. It posits that the external reality is a mathematical structure similar to the graph with 4 elements at the right side of Figure 02-15b. The human world creates artificial objects such as names and sports | |

## Figure 02-15b Mathematical Universe [view large image] |
(picture in the left panel) - some baggage not recognized universally. In mathematical universe, physical theories are here and everywhere; we just discover them and written them down in a form recognizable. |

- The theory of eternal inflation posits that the entire eternally inflating spacetime (false vacuum) originated as a minuscule closed multiverse. It tunneled, quantum-mechanically, out of nothing and immediately plunged into the never-ending inflation. Thus, the multiverse is eternal, but it did have a beginning. Inflation rapidly blows the universe up to an enormous size. It stopped where we are, producing our own island universe, and many others. But due to the peculiar structure of inflationary spacetime, it continues in other areas of the multiverse at large. The multiverse contains an unlimited number of island universes. We live in one of them, and our observable region is one of the infinite numbers of observable regions (at different locations) that it contains (see Figure 02-16a). We may be able to travel to the other observable regions, but we are forever confined to our own island universe. Constants of nature that shape the character
of our world take different values in other island universes. Most of these universes are drastically different from ours, and only a tiny fraction of them are hospitable to life. Figure 02-16b is another view of the same thing. The square represents an inflating volume, which decays into three with one of them turning into a non-inflating Big Bang universe. The result is a never ending process sprouting out entities like ours in number of 1, 2, 4, ... #### Figure 02-16a Multiverse, Eternal Inflation

#### Figure 02-16b Multiverse, Eternal Inflation 2 [view large image]

By 2006, the confluence of events has pushed many leading physicists toward the notion of a multiverse. These include: measurements that indicate the universe's expansion is accelerating; empirical tests that bolster the inflationary universe scenario; theories of eternal inflation (see above) that suggest an endless number of Big Bang; and developments in string theory that show how to design universes with widely different properties. In his 2011 book "The Hidden Reality - Parallel Universes and the Deep Laws of the Cosmos" Brian Greene summarizes nine different scenarios of multiverse in a table. All of them (except one) have been mentioned in various sections within this website. Table 02-04 is reproduced from the original in a different format below (Figure 02-16c is an artist's version of the multiverse): | |

## Figure 02-16c Cosmic Joy [view large image] |

Multiverse | Brief Description | Theoretical Base |
---|---|---|

Quilted | There must be repeated version of each universe in very large sample | Infinite size of the cosmos |

Inflationary | Bubble universes are created in eternal state of inflation | Theory of inflation |

Brane | Universes exist on 3-D brane | Theory of superstring |

Cyclic | Interacting braneworlds produce cycles of cosmic expansion | Theory of superstring |

Landscape | Universes reside in the valleys of the vacuum energy map | Theory of superstring |

Quantum | Multiverse is created by realization of all the quantum probabilities | Quantum Theory |

Holographic | Each universe has a holographic copy in a lower dimensional surface | Holographic principle |

Simulated | Universes can be simulated by very powerful computer | Advanced technology |

Ultimate | All possible mathematical equations have correspondence to some real universes | Philosophy |

He also missed the opening of a new exhibition on January 19, 2012 at the Science Museum entitled Stephen Hawking: A 70th Birthday Celebration. Figure 02-16d is a picture released by the London Science Museum showing him in his office at Cambridge University. Meanwhile in his absence, some scientists argued that some cosmological theories such as the inflationary and cyclic models (see Table 02-04) require a beginning to address the inconsistencies introduced by the limits on the | ||

## Figure 02-16d Hawking at 70 [view large image] |
## Figure 02-16e Cosmic Beginning |
Hubble constant and runaway entropy respectively (Figure 02-16e). Such findings always point to the necessity of supernatural creator contrary to the conclusion in Hawking's latest book: "The Grand Design". |

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