MadSci Network: Physics

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

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 

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 

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 
others, please let us know!


Jim Guinn

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