### Re: Two questions, one of black holes, and one of wave/particle duality

Date: Fri Aug 25 12:49:27 2006
Posted By: Jim Guinn, Staff, Science, Georgia Perimeter College
Area of science: Physics
ID: 1155746753.Ph
Message:
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Dear Andrew,

These are some great questions.  First, I'm with you!  But let me explain
a little bit, too.

The name 'black hole' was invented by John Archibald Wheeler to describe a
collapsed star whose escape velocity was greater than the speed of light.
An object's escape velocity is the speed at which something needs to be
moving in order to fly away from the object.  (As an example, the escape
velocity of the Earth is about 11 kilometers per second.)  The more
massive and compressed the object is, the greater its escape velocity.  A
black hole is so compressed, that within a certain distance from its
center, the escape velocity is faster than light.  This boundary between
where something could escape and where nothing can escape is called the
event horizon.  The radius of the event horizon for a non-spinning black
hole is called the Schwarzschild radius and can be calculated using the
equation

R = 2 G M / c2

Where R is the Schwarzschild radius, G is Newton's Gravitational constant
and has the value 6.67x10^-11 N m2/kg2, and c is the speed of light and has
the value 3.00x10^8 m/s .  To make this a little easier to use, if you take
an object's mass in kilograms, divide it by 6.75x10^26, you will get the
object's event horizon radius in meters.  For example, the Earth's mass is
about 5.97x10^24kg, so its event horizon is

5.97x10^24 / 6.75x1^26 = 8.85x10^-3m or 8.85 millimeters!

You would have to compress the Earth to the size of a small marble to turn
it into a black hole!

Your friend might be thinking that since light does not have any mass, and
that gravity is the force between two objects with mass, that light is not
affected by gravity.  This is not quite correct.  Isaac Newton, who
developed his Law of Universal Gravitation, did describe the gravitational
force between two objects with mass, and according to Newton's law, we
would expect light not to be affected by gravity.  However, Einstein's
Theory of Relativity gave us a deeper understanding of what gravity is.
He showed that what we experience as gravity comes about because of the
curvature of space-time.  In other words, when an object with mass is in
space, it curves the space around it and makes it seem that another near-
by body is pulled toward it.  This would affect light, too!  One of the
first experimental verifications of Einstein's Theory was to show that
during an eclipse of the Sun, star light really is bent by the Sun's
gravity!

So, since nothing (not even light) can travel faster than light, nothing
can get out from within the event horizon.  This was the reason that Dr.
Wheeler called these objects black holes; they emit nothing, not even
light, and so would appear black.  (Since that time, Stephen Hawking has
shown that there is a way that some energy can leak out from a black hole,
and this energy is called Hawking Radiation, but Dr. Wheeler didn't know
about that.)  This is true whether you are thinking about light as a wave
or a particle.  So what about wave-particle duality?

We tend to think of things as either a wave or a particle.  A wave is a
motion or disturbance that moves through some type of medium.  A water
wave, for example, is a disturbance that flows through water.  A wave, you
would think, aught to be able to carry a tiny amount of energy, a medium
amount of energy, a whole lot of energy, or anything in between.  Think
about lying on an inner tube in the ocean.  A little wave could move you
up and down a little, a big wave would move you a lot, and you could
imagine an infinite number of waves in between.  Light, on the other hand,
seems to be a disturbance that flows through the electromagnetic field.
(The electromagnetic field comes from the forces created by charged
particles like electrons and protons.)  In this sense, light is a wave.
When light interacts with matter, however, it seems to be able to give the
matter only certain amounts of energy.  A tiny bit, two tiny bits, three
tiny bits, etc, but nothing in between.  This is understood by the idea
that light comes in little bundles, called photons, and that you can have
one photon, two photons, three photons, but never anything in between.
This is where the particle idea comes in.  So how can light be a wave and
a particle?  It must be one or the other, right?  Wrong.  A better way of
thinking about light is that the wave part of the light tells us where we
might find the photons.  A big wave is a place that could have a lot of
photons, and a small wave is a place where we would expect to find fewer.
If all of this is a little confusing (or a lot confusing) don't worry!
Scientists are still trying to figure out exactly what light is and how it
interacts with matter.

If you would like to read some more about black holes and Einstein's
Theory of Relativity, I think a great book is 'Was Einstein Right?' by
Clifford Will.  It talks about relativity and what experiments have been
done to see if it is correct.  Another one is 'Black Holes and Baby
Universes and Other Essays' by Stephen Hawking.  You also might look for
other books by Kip Thorne, who wrote the book you mentioned.  He is an
excellent writer.

Well, Andrew, I hope I have answered your questions.  If you have any

Sincerely,

Jim Guinn

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