Black Holes In A Brief History by Niraj Pant (the reading list book TXT) 📕

Love Song of J. Alfred Prufrock”

Stephen Hawing’s A Brief History of Time recounts that in 1929, Edwin Hubble made the

observation that wherever you look, galaxies are moving rapidly away from us, just as the

Russian physicist, Alexander Friedmann had predicted they were. Friedman took Einstein’s then

recent theory of relativity more at face value, it seems, than even Einstein did, and accurately

described our universe as expanding evenly in every direction.

Hawking notes that, “Hubble’s observation suggests that there was a time, called the big bang,

when the universe was infinitesimally small and infinitely dense.”1

backward from a universe that is expanding in every direction, one arrives at a starting place

where it was all together before it began to expand. Conceptualize it like this: reverse an air

pump and suck the air out of a basketball and see the basketball collapse. Think of the big bang

in the same way, the universe is sucked in upon itself until gravity makes it, in Hawking’s words,

“infinitesimally small, infinitely dense.” If one comes upon a pool table with balls exploding

from the middle of it, he doesn’t have to be familiar with pool, which I am not, to know that the

balls were originally all together in the middle and something burst them apart.

We may assume the same thing about our expanding universe–probably it originally was tiny

and dense. Good that it began to expand, otherwise time and space would not exist and we would

not exist. But how that original spot came into existence before time and space; what it was

before time and space; and why it deployed into time and space is out of reach for anything but

speculation. Hawking says of the big bang:

At that time...the density of the universe and the curvature of space-time would have been

infinite. Because mathematics cannot really handle infinite numbers, this means that the

general theory of relativity predicts that there is a point in the universe where the theory

itself breaks down. In fact, all our theories of science are formulated on the assumption

that space-time is smooth and nearly flat, so they break down at the big bang singularity2

This singularity, this maybe-something-maybe-nothing, as a foothold, is a quandary for

cosmologists struggling to construct a ladder to the heavens–a unified theory of everything that

tells us what the universe is and perhaps what it was before time and space and why it became

the universe in time and space. Hawking says that in order to predict how the universe should

have started off, one needs laws that hold at the beginning of time. He and Roger Penrose proved

that if the classic theory of relativity is used as the model for how the universe started off, one

arrives at a point of infinite density and infinite curvature of space-time where all the known

laws of science break down–a singularity. But, by the use of quantum mechanics, Hawking says

that one may arrive at a model of how the universe started off and avoid the singularity. His own

personal model of how the universe started out has remained unproven since the nineteen-
eighties, but were it worked out, it is doubtful that it would tell us how the universe started off.

And no theory can tell us why.

Quantum mechanics, hard at work in the minutia all these years, is short sighted. It has a good

vision of the tiny, but can’t see into the distance far enough to make out where the pieces go

when they explode. The general theory of relativity, however, is far sighted. It describes the big

picture but can’t make out the nitty-gritty. The theories need to work together if they are to solve

the “small” that began at the big bang and became the “large” that is the present universe. As of

now they are involved in a family quarrel and are not compatible. Hawking believes that he can

devise a theory that will resolve their disagreement, but such a theory must meet his criteria for

what a good theory is:

In order to talk about the nature of the universe and to discuss questions as to whether it

has a beginning or an end, you have to be clear about what a scientific theory is. I shall

take the simple minded view that a theory is just a model of the universe, or a restricted

part of it, and a set of rules that relate quantities in the model to observation that we

make. It exists only in our minds and does not have any other reality (whatever that might

mean (his parenthesis)). A theory is a good theory if it satisfies two requirements: it must

accurately describe a large class of observations on the basis of a model that contains

only a few arbitrary elements and it must make definite predictions about the results of

future observations3

I lack the expertise to understand the theory of relativity or quantum mechanics. Given a lifetime

to study, I would lack the intellect to understand them. I must rely on scientists to tell me if and

when they resolve the differences between the general theory of relativity and quantum

mechanics. If these difficulties are resolved, Stephen Hawking probably will resolve them. If

someone else does, he has the intellect to understand how they did it. If Stephen Hawking says

the problems are resolved, I trust him to believe that they are. He knows all the theories out

there. Thus far Stephen has said nary a word about a resolution of the difficulties between

quantum mechanics and the general theory of relativity.

He does say, “We don’t yet have a complete and consistent unified theory that combines

quantum mechanics and gravity. But we are fairly certain of some features that such a unified

theory should have.” For clarity and brevity, we will avoid an explanation and description of

these features and just mention that they are Feynman’s sum over histories and Einstein’s idea

that the gravitational field is represented by curved space-time. All attempts to combine the

general theory of relativity with quantum mechanics have, to this day, failed. Should they have

succeeded, here is what Hawking assumes will follow:

When we apply Feynman’s sum over histories to Einstein’s view of gravity, the analogue

of the history of a particle is now a complete curved space-time that represents the history

of the whole universe.4

He concludes on the following page:

There would be no singularities at which the laws of science break down and no edge of

space-time at which one would have to appeal to God or some new law to set the

boundary conditions for space-time. One could say: ‘The boundary conditions of the

universe is that it has no boundary.’ The universe would be completely self-contained and

not affected by anything outside itself. It would neither be created nor destroyed. It would

just BE.5

BE what? Remember, this small dense particle is posited as existing before the big bang,

therefore before the existence of time and space and matter. Absent time, space and matter, there

are no particles to BE, and therefore no “large class of observations” upon which Hawking can

construct a model that makes “definite predictions about the results of future observations.”

Without those observations from which future observations can be made, Hawking’s theory fails

as a good scientific theory.

Hawking posits this infinitesimally small, infinitely dense particle from whence all other

particles – an infinite number of them perhaps – derived, as an analogue of the universe, an

analogy. But nowhere does his tiny ball stop being a tiny ball and become an analogy. He even

gives physical properties to this tiny ball:

Using the no boundary condition, we find that the universe must in fact have started off

with just the minimum possible nonuniformity allowed by the uncertainty principle...

This would lead to the formation of galaxies, stars , and eventually even insignificant

creatures like ourselves.6

Later in this book we shall see how fine tuned this minimum nonuniformity had to be in the first

billionth of a second into the big bang for there ever to be a universe like the one we experience,

but that is not the point of this chapter. Nor is “Insignificant creatures like ourselves.” We’ll

disregard the snub for now, noting only that intelligence is the most marvelous thing in creation,

and Hawking’s theory can’t be a theory that explains everything if it dismisses intelligence as

insignificant.

The point here is that Hawking is describing an analogy as if it were not an analogy at all, but a

thing the analogy was supposed to be like. Given such detailed characteristics of the ball, this is

no analogy, this is what Hawking thinks that infinitely tiny ball really was.

Granting that the non-uniformity necessarily existed in the infinitely small, infinitely dense

analogue of a universe and the analogue was ready to explode into the big bang, what was this

analogue? Stephen Hawking describes it as “finite in size but (does) not have any boundary or

edge.” Of course it is a contradiction to describe something as “infinitesimally small” and

“finite” in size. It can’t be both infinitely small and finitely small at the same time. This is not to

quibble, it is only to ask what Hawking means.

Disregarding this seeming contradiction, we blow up this small particle to see what it looks like:

It’s a sphere, a basketball. That is, an immortal ant could walk forever around a basketball and

come to no boundary or singularity--he would not fall off. This is the example that Hawking

gives of his infinitely small, infinitely dense ball, but instead of a basketball, he describes it as

being like the earth, which he says he traveled round without ever having run into a singularity or

an edge. One cannot conclude from such an analogy that the earth is infinite. I know personally

that basketballs are not, and they fit the same analogy.

Moreover, until this “infinitesimally small, infinitely dense” ball explodes, it does not exist, the

universe does not exist, space and time or space-time does not exist (a note here: “explode” is

inaccurate if one is made to think of bombs and firecrackers. Even though the big bang’s first

three second enlargement makes a detonation of TNT look as if it were in slow motion, its

deployment was near perfect in symmetry). Obviously the ball has not become the universe at

this point, has not deployed in the big bang. The universe that we know exists only in time and

space–it is time and space! But time and space did not come to exist until after the big bang, and

so the universe did not come to exist until after the big bang. Until the big bang, nothing exists.

To talk about any configuration that fits Hawking’s description of “finite in extent...(with no)

boundary or edge,” as if it existed before time and space, is to talk about it as if it existed before

existence, which makes as much sense as to say that because an immortal bug could crawl

around a basketball for eternity, basketballs are infinite.

It is unimportant what precisely the configuration was that Hawking uses the shape of the world

as an analogy of, but it is of utmost importance that it had a configuration. Things have

configuration, non-things don’t. When Hawking talks about that infinitely small, dense particle,

he is talking about something rather than nothing. It makes no sense for an analogue to be

analogous of nothing; no sense for a theory to be a theory about nothing. Keep in mind the

criteria Stephen Hawking says a good theory must conform to: It must describe a few arbitrary

elements, and from those observations, make predictions. “Infinitesimally small, infinitely

dense” describes something that exists. There was a time, he says, when all the galaxies were

together at the same place. What place did they exist in before space; what time before time?

We laymen are not limited by the limits that Hawking places on himself. His science can’t

describe something beyond time and space, and time and space did not exist beyond fourteen

billion years ago. His mathematics meets with a paradox, and mathematics does not deal well

with paradoxes.

But we laymen know how to handle paradoxes without resorting to mathematics. We simply

point to what we see must have happened in reality, and draw logical conclusions. Mathematics

is an indispensable tool, but it can’t explain how something came from nothing or describe how

something can exist forever. Hawking can’t describe this infinitely small dense ball as existing

forever, because forever began fourteen billion years ago for Hawking’s science.

If we are not careful, Hawking will roll that particle into an infinitesimally small, infinitely dense

ball and sneak it by us without