God and the Folly of Faith: The Incompatibility of Science and Religion (26 page)

However, the calculation is so obviously wrong that it should be ignored—certainly not taken as evidence for God. While physicists have not yet reached a consensus on the correct calculation, one possibility that agrees with observations is called the
holographic principle.
⁵³

The calculation of the vacuum energy density of the universe involves a sum over all the zero-point energy states in the universe. The “worst calculation ever” assumed that the number of states is proportional to the volume. But now there is reason to believe that this is wrong. The universe can have no more states than that of a black hole of the same size. The number of states in a black hole is proportional to its surface area, not its volume. So the holographic principle says that the number of states in the universe is proportional to the surface area of our event horizon. The energy density calculated from this assumption is of the same order of magnitude as the vacuum energy density that is determined from observations.

At the minimum, we can still conclude that it is certainly wrong to sum over the zero-energy states in the volume of the universe rather than on the surface. The fine-tuning of the cosmological constant is another God-of-the-gaps argument in which the gap is being filled in by some purely natural mortar.

Other Parameters

A systematic study of the remaining parameters that are claimed to be fine-tuned shows that their values all have plausible explanations within the framework of existing knowledge. They fall into four classes:

1. Basic physics constants

Three basic physics constants that are often claimed to be fine-tuned cannot be because their values are arbitrary, depending only on the system of units being used. These include the speed of light in a vacuum
c
, Planck's constant
h
, and Newton's constant
G.

2. The excited state of carbon nucleus

In 1952, astronomer Fred Hoyle used anthropic arguments to predict that an excited carbon nucleus,
₆
C
¹²
, has an energy level at around 7.7 million electron-volts, which was later confirmed by experiment.
⁵⁴
However, calculations show that a wide range of values for the energy level of that state produce sufficient carbon.
⁵⁵

3. Strengths of elementary forces

The strengths of the elementary forces are assumed in fine-tuning arguments to be constants that can take on a range of values that are then tuned for life. In fact, they vary with energy, and their relative values and energy dependences are close to being pinned down by theory in ranges that make some kind of life possible. When the standard model is supplemented by a concept called
supersymmetry
, the reciprocals of three strength parameters of the model vary linearly with the logarithm of energy and converge to a point at 3×10
¹⁶
GeV.
⁵⁶
Such an energy would have occurred during the early stages of the big bang.

4. Parameters of earth and solar system

Many parameters of Earth and the solar system are claimed to be fine-tuned for life.
⁵⁷
This fails to consider that with trillions of planets in the visible universe and the countless number beyond our horizon, a planet with the properties needed for life is likely to occur many times.

It is also to be noted that in almost all the literature that advocates fine-tuning, the authors make a serious analytical mistake by varying only one parameter at a time and holding all the others constant. This fails to account for the
fact that a change in one parameter can be compensated by a change in another, opening up more parameter space for a viable universe. A proper analysis finds there is no evidence that the universe is fine-tuned for us or anything else.

NATURAL ORIGINS

So far in this chapter we have discussed the arguments for the existence of a creator based on cosmology and shown why they are invalid. Then where did the universe come from if it was not divinely created? The truth is that we do not know. But that does not mean that science has nothing to say about the question or that a purely natural origin to our universe is beyond the reach of science.

Most popular books by physicists give a hand-waving argument in which the universe arises as a “quantum fluctuation” from the vacuum. These books usually give the example in which a particle-antiparticle pair, such as an electron and a positron, are created in a vacuum—a process known as “vacuum polarization.” The pair can have zero total energy, where the rest and kinetic energies of the particles are balanced by the electromagnetic and gravitational potential energies, in agreement with the observations mentioned previously in which the current energy density of the universe is balanced in just this way. However, theologians point out that the initial state of a vacuum is not the “nothing” that is associated with nonexistence. Rather, it is a perfectly definable physical state with particle pairs popping in and out of existence all the time. They reasonably ask, where did that state come from? The simplest answer is that it always existed, so it didn't have to come from anything. As we saw above, the argument that the universe can't be eternal is erroneous and, furthermore, an eternal multiverse is suggested by modern cosmology.

Let us go beyond hand waving and discuss some serious attempts that have been made to provide plausible scenarios for the natural origin of our universe. A number of models exist for an uncreated origin of the visible universe that have been published by reputable scientists in reputable, peer-reviewed journals.
⁵⁸
They all are presented in mathematical detail and are consistent with established physics and cosmology. Rather than discuss all these models here, let me simply describe one straightforward scenario that utilizes
a well-established mechanism called
quantum tunneling
that appears in physics in other contexts.

QUANTUM TUNNELING

Quantum tunneling is worked out mathematically in most lower division college physics textbooks. In classical physics, an object cannot surmount a barrier if its kinetic energy is less than the potential energy at the top of the barrier. However, in quantum mechanics, the mathematics of the Schrödinger equation allows a solution inside the barrier in which the wave function is not zero.

Normally, physical quantities such as a body's momentum and kinetic energy are defined “operationally” by how they are measured and the resulting measurements are represented by
real
numbers whose squares are positive. Inside the barrier, however, such quantities are represented mathematically by
imaginary
numbers, that is, numbers whose squares are negative. They are what we call
unphysical.
We can't measure them, but we can still talk about them mathematically. The wave function given by Schrödinger's equation, which I have emphasized is just an abstract mathematical object, simply has imaginary momentum and kinetic energy.

When we cross the opposite side of the barrier we return to the physical region where measurements can again be made. Schrödinger's equation gives us a solution in which quantities are once again real numbers and the probability for the object leaking through the barrier is nonzero. In short, quantum tunneling allows a physical body to pass through a wall. While that probability is very low on the everyday scale, which is why we don't witness people walking through walls, it happens on the subatomic scale and has been firmly established empirically. In an important example, the nuclear fusion process, in which two hydrogen nuclei combine to produce energy, results from the nuclei quantum-tunneling through the repulsive barrier that separates them due to their positive electric charges. Since fusion is the prime source of the sun's energy, we would not be here if it were not for quantum tunneling. The scanning tunneling microscope, mentioned earlier, with which we can see individual atoms, is an application of quantum tunneling.

TUNNELING FROM (OR THROUGH) NOTHING

Now let us apply quantum tunneling to the origin of our universe. To my knowledge, Vilenkin first worked this notion out mathematically in 1982.
⁵⁹
An excellent account can be found in his 2006 popular book
Many Worlds in One: The Search for Other Universes
.
⁶⁰

Vilenkin's scenario calls for our universe tunneling out of “nothing,” which he takes to be the region of chaos that existed before the big bang. However, trying to define “nothing,” as we have seen, is a contentious matter. As with the quantum fluctuation model described above, cosmic creationists simply say that Vilenkin's “nothing” is still something that exists and so does not answer the question of how the universe came into existence from “nonexistence.”

So, for my purposes here, I am going to avoid the issue by having our universe tunnel from “something,” namely a prior universe that always existed. As we saw above, we have no reason to rule out an eternal multiverse.

We can envisage an earlier universe that is more or less a mirror of ours, on the opposite side of the time axis where the origin is at
t
= 0. Such a universe is not forbidden by any known principle and, furthermore, is accommodated by the same cosmological equations that we use to describe our universe. Just insert a negative
t
in the equations.

According to those equations, this earlier universe contracts down until it becomes as small as it can be according to quantum mechanics, a sphere of radius equal to the Planck length, 1.62×10
^–35
meter. At that point it has maximum entropy, as discussed earlier, and forms a region of total chaos.

However, like the region inside a barrier, this region of chaos is in an “unphysical” state, absent of any observable structure but which still can be described mathematically. The wave function of the universe (a well-defined quantity, believe it or not)
⁶¹
is able to tunnel through the chaos and reappear on the other side of the time axis and become our expanding universe.
⁶²

Now this scenario is not to be confused with older proposals about an “oscillating universe” in which our expansion is followed by a contraction and then by another expansion, ad infinitum. That proposal fails because of the second law of thermodynamics. The direction of increase in entropy of the
universe does not reverse during the contracting phase but keeps increasing and eventually hits the limit of total chaos long before the universe has collapsed back to Planck dimensions.

In the new scenario, our mirror universe is only contracting from our point of view. Since, as we saw in
chapter 5
, the arrow of time is defined by the direction of increasing entropy, time's arrow in the mirror universe will point opposite to ours. Thus we can view the two universes as emerging from the central chaos and expanding in opposite directions. Theologians have not come to grips with the fact that time can flow in either direction. The whole notion of a creator assumes a unidirectional flow of time.

So, in this scenario, we do not have to explain how our universe came from “nothing.” From our point of view in this universe, it tunneled from an earlier universe. Where did that earlier universe come from? From its point of view it tunneled from our universe.

Now, I do not claim that this is exactly how it all happened. But the fact that such a scenario can be fully formulated, with mathematical rigor based on existing knowledge, suffices to refute any claim that a miraculous creation necessarily occurred.

THE GRAND ACCIDENT

Stephen Hawking is no doubt the most celebrated scientist in the world. Deservedly so, since he has for decades made outstanding contributions to physics and cosmology and to their public understanding, while suffering from amyotropic lateral sclerosis that leaves him almost completely paralyzed. I have frequently referred to his 1988 bestseller
A Brief History of Time
.

More recently he has published another bestseller,
The Grand Design
, written with physicist Leonard Mlodinow.
⁶³
Hawking's books, given their great exposure, usually lead to a media emphasis on what the books say about nonscientific issues, in particular, religion. In
Brief History
, Hawking stirred the pot by referring to God in many places. In his final paragraph of that book he talks about someday discovering a complete theory that tells us why it is that we and the universe exist. His concluding sentence: “If we ever find the
answer to that, it would be the ultimate triumph of human reason—for then we would know the mind of God.”
⁶⁴

Of course this was interpreted as meaning that Hawking believed in God. But he was misunderstood the way Einstein was frequently misunderstood when he mentioned “God” in his utterances. Both asserted their nonbelief in a personal God in no uncertain terms and were simply using the word “God” in the Spinozian sense as a name for the order of the universe.

In the introduction to
Brief History
, Carl Sagan explicitly summarized Hawking's main proposal: “A universe with no edge in space, no beginning or end in time, and nothing for a creator to do.”
⁶⁵
This refers to a model for the origin of the universe called the
no-boundary model
, which Hawking published in 1983 along with James Hartle.
⁶⁶
The tunneling scenario presented earlier is a modified version of the Hartle-Hawking model. Their wave function is simply extended to the negative side of the time axis.

Hawking's new book is not just another gee-whiz recitation of recent developments but a profound proposal for the nature of reality that turns on its head the conventional view of how physics operates. Philosophers of science will give it a lot more attention than physicists, who generally tune out such discussions.