Labyrinths of Reason (12 page)

Few would argue with Russell, for the same reasoning quashes any proposed refutation. A 1945 bottle of Château Latour—the yellowed pages of a Gutenberg Bible, dated 1457—fossils—carbon 14 dating—astrophysical evidence of the age of stars—the Hubble time—none means anything more than the time on a clock in a painting. They were simply created that way, five minutes ago.

(In a weird case of theology imitating philosophy, some opponents of Darwinian evolution have claimed that God created fossils to tempt the wicked into disbelieving that the world was created in 4004 B.C., as Archbishop Ussher figured in the margins of the King James Bible.)

The antirealist position can be applied unwisely. There is always the danger of assuming too readily that something presently unknowable must remain so forever. In 1835 French philosopher and mathematician Auguste Comte, founder of logical positivism, advanced the chemical composition of stars as something necessarily beyond human knowledge. “The field of positive philosophy lies wholly within the limits of our solar system,” he wrote.

Not only was Comte wrong; he was untimely. As he wrote those words, physicists were puzzling over the mysterious dark lines Joseph von Fraunhofer had discovered in the sun’s spectrum. A generation later, Gustav Kirchhoff and Robert Bunsen realized that the lines were produced by chemical elements in the sun. When the spectroscope was pointed at a distant star, it would reveal the star’s chemical composition as well.

One scientific topic often cited in discussions of antirealism is black holes. It is sometimes asserted that predictions about the interiors of black holes are unverifiable and thus open to the antirealist claim that the predictions are meaningless. This is not strictly true, and it may be useful to examine why.

A black hole is a region of space with such an intense gravitational field that nothing which enters can ever leave. The “nothing” is absolute and final. Neither matter nor energy of any kind can get out. Since even information must be conveyed in matter or energy, not even information can exit a black hole.

Think about that: There is no way for someone inside a black hole to send a radio signal to us; no way to put a message in a bottle
and propel it out. We on the outside can never know anything directly about whatever goes on inside a black hole. Does it make any sense, then, to talk of what happens inside a black hole?

Black holes are a prediction of Einstein’s theory of gravity, the general theory of relativity. This theory
does
make predictions about the interior of black holes—as well as virtually guaranteeing that those predictions can never be tested. A black hole results whenever a great enough mass is concentrated in a small enough space. When a large star (about twice the size of our sun or bigger) runs out of thermonuclear fuel and collapses, its own gravity will compress it ever smaller and smaller. The more compact it gets, the more intense its gravitational field becomes. Once the gravity passes a critical point, no force known to physics can stop it. The atoms are crushed out of existence. The star shrinks to (as far as anyone knows) a point.

Though the star disappears, its gravity remains. It leaves behind an intense gravitational field, the black hole. The “boundary” of a black hole is called the
event horizon
. This is the literal point of no return. Anything that plunges within this spherical boundary can never come out again.

A black hole would be spherical and typically only miles in circumference; it would be utterly, totally black; and it would warp the light of any objects behind it, something like a bubble in a pane of glass. A typical stellar black hole resulting from the complete collapse of a star twice the sun’s mass would have an effective diameter of twelve kilometers (seven miles). This effective diameter is a fiction. To measure a black hole’s diameter (or radius) you would have to stretch a measuring tape or equivalent
inside the black hole
. Any observer who did that could never report the measurement to the outside world. Besides, this diameter is theoretically infinite through the warping of space. What one can do is measure the circumference of a black hole. In principle you can do this by looping a measuring tape around the black hole, just outside the event horizon. Dividing this circumference by pi gives the effective diameter—a measure of the space the black hole seems to occupy, to observers in the outside world.

Let’s examine several schemes for getting information out of a black hole. It would do no good to send in a NASA-style probe that relays data back via radio. Radio waves, like visible light, are a type
of electromagnetic radiation. A radio signal can no more emerge from a black hole than can a flashlight beam.

Another easily dismissed scheme is to send a rocket in and out. Any planet or star has an escape velocity. A rocket must exceed the escape velocity to leave the body without falling back. For a black hole, the escape velocity is the speed of light. Since the speed of light is a cosmic speed limit that nothing can exceed, no possible rocket design could extricate itself from a black hole.

You can imagine rigging up a bathyscaphlike probe. The probe, fitted with searchlights and cameras, is lowered into a black hole on an absolutely unbreakable cable. The cable is anchored to—well, something really big and solid. The probe snaps some pictures, then it’s pulled back out.

It wouldn’t work. Once an atom of cable is inside the event horizon, no physical force, including the electromagnetic forces that hold matter together, can transport the atom outside again. There can be no such thing as an “absolutely unbreakable” cable in a universe that contains black holes.

Agreed, then, that nothing that goes into a black hole ever comes out again. That does not necessarily mean that predictions about black-hole interiors are unverifiable. In principle, a person could go inside a black hole and take a look around. He could never come out again, and he would not survive long on the inside. It would furthermore have to be a very large black hole, or the observer could not even survive crossing the event horizon.

The distortion of space around a black hole takes the form of an immense tidal force. This is the same type of force that creates the tides on earth. The moon’s gravity tends to elongate and compress the earth. Rock yields less to this force than water, so we notice tidal bulges of the oceans.

The fantastic tidal force near a black hole also tends to stretch any object in the radial direction and compress it in the other directions. Picture yourself floating in space, your feet pointing to a black hole and your head away from it. Tidal forces would stretch you from head to foot, and crush you from the sides.

Identical forces would be felt by a rocket or any other object. The forces at the event horizon of a black hole a few times more massive than the sun would certainly be enough to kill a person, and possibly enough to destroy a sizable object of any known material. No one could survive approaching, much less entering, a typical-size black hole.

Black holes come in different sizes. The size of the black hole (or,
more exactly, of its boundary, the event horizon) depends on the mass of the object that created it. Ironically, the tidal forces at the event horizon are
less
for more massive black holes.

According to general relativity, the tidal forces at the event horizon decrease in inverse proportion to the square of the black hole’s mass. It has been estimated that a human body could withstand the tidal forces existing at the horizon of a black hole with a mass about a thousand times that of the sun. No known star is that big, but it is suspected that there are black holes much bigger yet.

In 1987 astronomers Douglas Richstone and Alan Dressier reported evidence that massive black holes may exist in the center of the Andromeda galaxy and its satellite galaxy, M32. They found that stars near the galaxies’ centers were orbiting much faster than expected. In the case of the Andromeda galaxy, this could be explained if the stars were orbiting an unseen, relatively compact object with a mass about 70 million times that of the sun. Among known and theoretical objects, that could only be a black hole. Other, more indirect evidence suggests that a similar black hole may exist in the center of our own galaxy. The tidal forces at the event horizon of such a black hole would be mild—about 5 billion times less than that of a 1000-solar-mass hole. A person could easily survive the tidal forces outside a galactic black hole and for some distance inside.

At the center of a black hole is a “singularity,” a point of infinite compression and infinite curvature of space-time. Any object that crosses the event horizon is pulled to the singularity. For an observer, reaching the singularity is the end, no matter what. No body or device can withstand infinite tidal forces.

The time it takes to reach the singularity depends on the size of the black hole. It works out to 1.54×10
^×5
seconds times the mass of the black hole divided by the mass of the sun. (This is the time measured by the infalling observer. To other observers, the time interval is different. In the frame of reference of an observer at rest far from the black hole, the fall takes—literally—forever. This is another effect of the profound distortion of time and space around a black hole.)

For a typical black hole of two solar masses, the travel time from event horizon to singularity would be about 3×10
^×3
second. For a black hole of 1000 solar masses, the maximum time of fall would be 0.0154 seconds. In either case, an observer would be dead by the time he crossed the event horizon.

However, for a 70-million-solar-mass black hole, such as might
exist in the heart of the Andromeda galaxy, the time is 1100 seconds (18 minutes). Tidal forces would remain bearable for nearly all of the 18-minute fall to the singularity. Certain death would come only in the last split second.

The ultimate fate of someone entering a black hole is surrealistically gruesome. In the last moments before hitting the singularity, tidal forces would increase without limit. Bone and muscle would give way, followed by cellular and atomic structure. You would be spun into a spaghetti strand of ever-increasing length and ever-decreasing diameter. The strand would become thinner than the finest thread while stretching to infinite length (the radius of a black hole is infinite from the inside). The final volume would be zero. A human body that enters a black hole is transformed into Euclid’s ideal line.

(The infalling observer’s view of all this would probably be disappointing. You would want, I guess, to see the singularity, or at least to see all the previously consumed objects that have been deformed into radial needles of zero volume. Unfortunately, the light from all previously consumed objects, including the stars that formed the black hole, can never reach a later infalling observer. You could only see objects that crossed the event horizon after you. Like Brahma, the singularity is visible to no observer until he becomes part of it.)

The experiment could not be popular, but its conceivability has bearing on the “reality” of black-hole interiors. There would be time for an infalling observer to take photographs, do experiments, write about the experience in a diary. To the observer, there would be no doubt about the reality of the experience.

The catch is that there is no possibility whatsoever of the observer communicating his experiences to us on the outside. The experience cannot be incorporated into the body of shared human experience. Does this make a difference? If you think it does, suppose the earth falls into this galactic black hole. For 18 minutes,
everyone
would be conscious of being inside a black hole.

One feels strongly that all this demonstrates that black-hole interiors
are
real (provided general relativity is right). There is a big difference between a hypothesis that no one could confirm, no matter what (like Poincaré’s nocturnal doubling), and one that is only very difficult—even suicidal—to test (the astrophysics of black-hole interiors). The realm of science is testable hypotheses—hypotheses that somehow “make a difference.” Poincaré’s doubling is a phantasm because there would be no difference. In contrast, if you entered
a black hole, something would happen, and that something would either confirm or refute general relativity.

Cognitive science, the study of mind, deals in many untestable entities. The venerable “other minds” problem of philosophers asks how we know that other people have thoughts and feelings as we do. Everyone else
could
be a robotlike being programmed to talk and react, but feeling nothing. What can you do to demonstrate that this is not so?

The “other minds” problem can be formulated as a Poincaréesque thought experiment. Suppose that last night everyone except you lost their soul/consciousness/mind. They still act the same way, but the internal dialogue, so to speak, is completely gone. Is there any way of telling that this has happened? (Or assume that half the people in the world have souls and the other half don’t. How do you tell who does and who doesn’t?)

Certainly other people talk about their loves, hates, pains, and joys. That proves nothing. We have to assume that all the observed diversity of human behavior is within the ken of the unconscious automatons. If other people’s consciousness is an illusion, it is a good illusion.

What you want is some clever question that would catch the alleged robots off guard and reveal their lack of true emotion. You could say that the fact that other people have thought up and discussed the “other minds” problem is proof that they have minds. Robotlike beings would not care, or even suspect, that there might be true consciousness. This fails to give the hypothetical robots enough credit.

There is inductive reason for belief in other minds. In many, many ways, each of us learns that we are similar to the five billion other members of the human race. Since each of us (presumably) knows he has a mind, it is natural to project that attribute onto everyone else. This is shaky induction, for it is extrapolating from just one known mind. Hence the question about finding an objective test.