Hubble reported that the galaxies are moving away from one another at speeds approximately proportional to their distance, indicating that the universe is expanding. This provided the earliest evidence for the big bang. For our purposes, an expanding universe could have started in total chaos and still formed localized order consistent with the second law.
The simplest way to see this is with a (literally) homey example. Suppose that whenever you clean your house, you empty the collected rubbish by tossing it out the window into your yard. Eventually the yard would be filled with rubbish. However, you can continue doing this with a simple expedient. Just keep buying up the land around your house and you will always have more room to toss the rubbish. You are able to maintain localized order—in your house—at the expense of increased disorder in the rest of the universe.
Similarly, parts of the universe can become more orderly as the rubbish, or entropy, produced during the ordering process (think of it as disorder being removed from the system being ordered) is tossed out into the larger, ever-expanding surrounding space. As illustrated in figure 4.1, the total entropy of the universe increases as the universe expands, as required by the second law.[38] However, the maximum possible entropy increases even faster, leaving increasingly more room for order to form. The reason for this is that the maximum entropy of a sphere of a certain radius (we are thinking of the universe as a sphere) is that of a black hole of that radius. The expanding universe is not a black hole and so has less than maximum entropy. Thus, while becoming more disorderly on the whole as time goes by, our expanding universe is not maximally disordered. But, once it was.
Suppose we extrapolate the expansion back 13.7 billion years to the earliest definable moment, the
This requires further elaboration. I seem to be saying that the entropy of the universe was maximal when the universe began, yet it has been increasing ever since. Indeed, that’s exactly what I am saying. When the universe began, its entropy was as high as it could be for an object of that size because the universe was equivalent to a black hole from which no information can be extracted. Currently the entropy is higher but not maximal, that is, not as high as it could be for an object of the universe’s current size. The universe is no longer a black hole.
I also need to respond here to an objection that has been raised by physicists who have heard me make this statement. They point out, correctly, that we currently do not have a theory of quantum gravity that we can apply to describe physics earlier than the Planck time. I have adopted Einstein’s operational definition of time as what you read on a clock. In order to measure a time interval smaller than the Planck time, you would need to make that measurement in a region smaller than the Planck length, which equals the Planck time multiplied by the speed of light. According to the Heisenberg uncertainty principle of quantum mechanics, such a region would be a black hole, from which no information can escape. This implies that no time interval can be defined that is smaller than the Planck time.[39]
Consider the present time. Clearly we do not have any qualms about applying established physics “now” and for short times earlier or later, as long as we do not try to do so for time intervals shorter than the Planck time. Basically, by definition time is counted off as an integral number of units where one unit equals the Planck time. We can get away with treating time as a continuous variable in our mathematical physics, such as we do when we use calculus, because the units are so small compared to anything we measure in practice. We essentially extrapolate our equations through the Planck intervals within which time is unmeasurable and thus indefinable. If we can do this “now,” we can do it at the end of the earliest Planck interval where we must begin our description of the beginning of the big bang.
At that time, our extrapolation from later times tells us that the entropy was maximal. In that case, the disorder was complete and no structure could have been present. Thus, the universe began with no structure. It has structure today consistent with the fact that its entropy is no longer maximal.
In short, according to our best current cosmological understanding, our universe began with no structure or organization, designed or otherwise. It was a state of chaos.
We are thus forced to conclude that the complex order we now observe could
Once again we have a result that might have turned out otherwise and provided strong scientific evidence for a creator. If the universe were not expanding but a firmament, as described in the Bible, then the second law would have required that the entropy of the universe was lower than its maximum allowed value in the past. Thus, if the universe had a beginning, it would have begun in a state of high order necessarily imposed from the outside. Even if the universe extended into the infinite past, it would be increasingly orderly in that direction, and the source of that order would defy natural description.
The empirical fact of the big bang has led some theists to argue that this, in itself, demonstrates the existence of a creator. In 1951 Pope Pius XII told the Pontifical Academy, “Creation took place in time, therefore there is a Creator, therefore God exists.”[40] The astronomer/priest Georges-Henri Lemaitre, who first proposed the idea of a big bang, wisely advised the pope not make this statement “infallible.”
Christian apologist William Lane Craig has made a number of sophisticated arguments that he claims show that the universe must have had a beginning and that beginning implies a personal creator.[41] One such argument is based on
In 1970 cosmologist Stephen Hawking and mathematician Roger Penrose, using a theorem derived earlier by Penrose, “proved” that a
However, Hawking has repudiated his own earlier proof. In his best seller
Craig and other theists also make another, related argument that the universe had to have had a beginning at some point, because if it were infinitely old, it would have taken an infinite time to reach the present. However, as philosopher Keith Parsons has pointed out, “To say the universe is infinitely old is to say that it had no beginning—not a beginning that was infinitely long ago.”[45]
Infinity is an abstract mathematical concept that was precisely formulated in the work of mathematician Georg Cantor in the late nineteenth century. However, the symbol for infinity, “©,” is used in physics simply as a shorthand for “a very big number.” Physics is counting. In physics, time is simply the count of ticks on a clock. You can count backward as well as forward. Counting forward you can get a very big but never mathematically infinite positive number and time “never ends.” Counting backward you can get a very big but never mathematically infinite negative number and time “never begins.” Just as we never reach positive infinity, we never reach negative infinity. Even if the universe does not have a mathematically infinite number of events in the future, it still need not have an end. Similarly, even if the universe does not have a mathematically infinite number of events in the past, it still need not have a beginning. We can always have one event follow another, and we can always have one event precede
