My January 8 column was mostly about Stephen Hawking. After
I posted the column, Brian Trumbore called my attention to a
January 7 New York Times article discussing a weeklong
celebration of Hawking”s 60th birthday at Cambridge University.
According to the article, Hawking”s survival for so long with Lou
Gehrig”s disease, ALS, has sparked interest and controversy in
medical circles. Some think Hawking has a special genetic
makeup that slows the progress of the disease. Others question
whether Hawking has ALS at all. They feel that it could be
something like spinal muscular atrophy, a less deadly malady.
Whatever the answer, there”s no question that Hawking has
labored admirably with a daunting physical handicap.
I have now finished reading Hawking”s “The Universe in a
Nutshell”. Notice that I did not say that I understood what it was
that I read! However, I do feel a tiny bit more comfortable with
two concepts that still boggle my brain. One is the idea of
“virtual” particles popping in and out of existence from nothing
in what we normally think of as “empty” space. The other
concept is the idea for which Hawking is famous – that black
holes are not really black and that they eventually evaporate and
disappear. These two concepts are closely connected.
WARNING – my wife says that the following is much too
complicated. I totally agree, but I”ve stated before that one
reason I write these columns is that if I write about some
complex subject I might delude myself into thinking that I
understand it! I have not succeeded in the following but hey,
maybe next time!
The idea of making something out of nothing in empty space is
really bothersome. Hawking”s description of himself as a
“positivist” helps me to accept such an outlandish idea. A
glossary at the end of Hawking”s book defines the “positivist”
approach as the “idea that a scientific theory is a mathematical
model that describes and codifies the observations we make.”
This definition doesn”t thrill me particularly. After reading the
book, I”ve decided that another way to describe positivism is “If
it works, don”t fix it!”
Suppose you have a mathematical theory and the theory agrees
with everything you know and observe. In addition, you use it to
predict things and find, sure enough, the predictions are correct.
If you”re a positivist, you accept whatever assumptions went into
the theory unless you observe something that disagrees with it.
That”s when you try to fix it by coming up with a new theory.
Quantum mechanics is a successful theory that involves some
very weird assumptions. Yet, quantum mechanics has survived
the test of time for almost a century. Indeed, some of the
weirdest assumptions and conclusions have been confirmed only
recently.
Back to those virtual particles that form from nothing. Don”t
start looking for them. It would be a waste of time. They have
never been detected and never will be. But Hawking says that
the mathematics can be interpreted as virtual particles. So let”s
be positivists and go along with Hawking and his fellow
theorists. It seems that one of the key reasons that these particles
are believable is Heisenberg”s uncertainty principle.
Back in the year I was born, 1927, this fellow Werner
Heisenberg came up with a very profound and important finding.
He showed that you can”t measure both the position and speed of
a particle precisely. Why? He showed that the measurement
itself disturbs the particle. The more precisely you measure the
position the more uncertain the speed that the particle is moving
and vice versa. This is one of the weird facets of quantum
mechanics that even Einstein had trouble accepting. The
uncertainty principle doesn”t affect us in our normal course of
events but for the atomic world it”s hugely important.
For example, let”s look at a spot far out in “empty” space. We
say that there is absolutely nothing in that empty bit of space.
But wait, remember Heisenberg and that you can”t say that a
particle is absolutely precisely in a certain spot. There has to be
some uncertainty. If I interpret Hawking correctly, Heisenberg”s
uncertainty also means that you can”t say a particle (or a field)
absolutely precisely is NOT in a certain spot! (I may be totally
wrong, but maybe this follows in that if you could say it wasn”t in
one spot, you could also say it wasn”t in other spots. If you had
enough time and patience you could say it wasn”t anywhere but
the exact spot you thought it was. This would certainly offend
Heisenberg!)
If you can”t say there is no particle or field in a given spot in
empty space, you shouldn”t be surprised that there are particles
there popping in and out of existence. Ok, I”ll be the first to
admit that I”m still quite surprised but maybe a tad less so than
before reading the book and searching the Web. (In addition to
Hawking”s book, I found the Web site of the Stanford Linear
Accelerator Center (SLAC) at Stanford University was especially
informative about virtual particles.)
The thinking is that actually two of these particles pop up
together, one having positive energy and the other negative
energy. Don”t ask me to define positive and negative energy, I”m
just taking Hawking”s word for it. Well, if one has positive
energy and one has negative energy, as they say, opposites attract
and sure enough, the two particles get together and poof, they”re
gone! These particles are so tiny and pop in and out of existence
so fast that you never know they”re there. In fact, everything I
read says these particles are not “real” and you can only detect
real particles. Remember we have to be positivists about this.
Even if we can”t see them, virtual particles have been around for
some time in various theories and are even thought to be
responsible for such things as why oppositely charged particles
attract each other or particles of the same charge repel each
other. And the theories work!
What does this have to do with black holes not being black?
First, remember that black holes form when stars heavier than
our sun run out of fuel to fire up their nuclear furnaces and the
star collapses. The collapsing star”s gravity is so strong that
anything in its vicinity is sucked in and even light can”t escape.
However, a black hole has this feature known as the event
horizon. This is the location around the black hole where light is
not trapped and just manages to escape. If an astronaut were
falling toward a black hole the last place you”d see him or her
would be at this event horizon.
Hawking is especially noted for what he says happens at this
event horizon. Suppose a couple virtual particles pop up in the
space very close to this event horizon. Now suppose the particle
with negative energy gets sucked into the black hole but the other
one with positive energy goes flitting off, escaping the black
hole”s grasp. What”s the result of this weird happening?
Remember that Einstein”s famous equation says that energy and
mass are equivalent. But we”ve just added a teensy bit of
negative energy to the black hole. If we add negative energy this
must mean that the energy of the black hole has gone down a
teensy amount. Since mass and energy are equivalent, this also
means that the mass of the black hole has gone down a teensy
bit. Continue this process with zillions of virtual particles for
zillions of years and the black hole has evaporated!
Hawking says that we should be able to see the radiation
corresponding to those virtual particles that have escaped the
clutches of the black hole. If they escaped, it seems that now
they”re “real” particles! Go figure! The unfortunate thing is that
the temperature corresponding to this “Hawking radiation” for
your common everyday black hole is millionths of degree
Kelvin. But we”ve discussed before that we”re all being
continually bombarded with cosmic background radiation left
over from the Big Bang. Sadly, this cosmic radiation is
everywhere and, with a temperature of nearly 3 degrees Kelvin,
swamps something as cold as millionths of a degree coming from
the black holes. You would never see it. Pity poor Hawking.
He says that he would get the Nobel Prize if someone could spot
his radiation. Perhaps his grandson, whose picture is in the book,
will be clever enough to figure out a way to confirm his PopPop”s
theory. (I don”t really know that his grandson calls him PopPop
but mine calls me that.)
I”m hoping to hear what Hawking had to say on the occasion of
his 60th birthday. He laments the fact that his speech synthesizer
gives him an American, rather than his native British accent. I
suspect that he could really correct that problem if he put his
mind to it! However, black holes are probably more important.
Allen F. Bortrum
