From: Ronald Wong (ronwong@inreach.com)
Date: Tue Apr 12 2005 - 16:22:20 PDT
Message-Id: <l03102800be8205324873@[209.209.14.20]> Date: Tue, 12 Apr 2005 16:22:20 -0700 From: Ronald Wong <ronwong@inreach.com> Subject: Electrons and Black Holes
I recently was asked to answer a number of questions relating to the
electron and I thought pinholers might find the the response of interest.
>Hi Ron,
>
>One of my classmates in an online General Relativity class has asked
>"Why isn't an electron a black hole?" My response was "How do we know
>it isn't?" and "What's an electron?"
>...
Let's take the second question first:
*********************
>My response was "How do we know it isn't [a black hole]?"
We know that it isn't. The reason lies in the answer to your classmate's
question (the first question):
*********************
>"Why isn't an electron a black hole?"
It's a matter of mass.
Around 5 billion years ago, there was enough mass in this region of the
universe to allow gravity to condense it into a ball of gas wherein the
pressure and temperature at it's center was high enough to trigger the
thermonuclear change that brought it to light and allowed it to evolve into
the star that we see today - the sun.
Stars that are formed with significantly less mass, like the nearby star
known as Bernard's star (it's the next one beyond the stars that form the
Alpha Centauri group and is around 1/10th of a solar mass), give off most
of their energy in the infrared and are known as red dwarfs. Over a very
long time, they will cool down and become black dwarfs.
Our sun - and other stars up to around 1.4 times the sun's mass - will, in
time, swell up into red giant for a brief period of time and, after blowing
off it's outer atmosphere, collapse into a white dwarf. It will be about
the size of the earth - ~10^4 km across - and a million times denser than
water. At this point, the force of gravity will have shrunk the sun down to
such a small size that the electrons will have run out of room to move
around in (thus preventing further collapse). The surface temperature will
be 10 times what it is now and, since the nuclear process that was
responsible for all the heat and light will have ceased, it'll simply begin
to cool down. In 10 billion years it will become a black dwarf.
NOT a black hole, just a black dwarf.
If the mass of a star is between 1.4 and 3 solar masses, the force of
gravity will be so great that it will fuse the electrons with the protons
and form neutrons. Like the electrons in the white dwarf, these neutrons
will find that the force is so great that they do not have enough room to
run around in. The star will have become a single, massive ball of
neutrons. Since these are neutrons, they can be packed more closely
together than the "atoms" of the white dwarf. Though far more massive than
the sun, the size of the neutron star will be ~20 km across - 1/500th the
size of a white dwarf - and thus far denser than the white dwarf (around
10^14 times the density of water). The amount of energy in these stars is
staggering and it'll be a very long time before they cool down and
disappear from view.
But we still won't have a black hole. In the end, all we'll have is a cold,
dead neutron star.
To get a black hole, the star has to have a mass greater than 3 solar
masses. With that much mass, nothing can prevent the star from collapsing
in on itself and forming a black hole.
With a mass of only 9 X 10^-31 kg, an electron falls far short of the mass
needed to form a black hole - by a factor of 10^60.
BUT...
Einstein said that energy is equivalent to matter. So, how much energy is
equivalent to 3 solar masses? The value is staggering but some enterprising
physicists have crunched the numbers and are arguing that the particle
accelerator being built at CERN in Geneva (LHC - due for completion in
2007) should have enough energy to produce several black holes a second.
They won't be large (10^-9 kg - a mote) and they won't last long (10^-26
seconds) but they'll be there IF enough energy can be packed into a region
one millionth the size of the nucleus of an atom (this is just a few orders
of magnitude smaller than the size of a classical electron so, contrary to
appearances, I really haven't gotten off topic).
Actually, the energy of the LHC will be a million billion times LESS than
that needed BUT, these physicists argue, IF we really live in a
multi-dimensional universe AND gravity leaks away into these other
dimensions (which is why it's as weak as it is in our 3 dimensional world -
according to "them") then, because the dimensions of this experiment will
be too small for gravity to "leak away", the gravitational force will have
more then enough strength to create mini-black holes in the heart of their
collider.
It's all smoke and mirrors but so was the concept of anti-matter early in
the last century. We'll have to wait and see what happens.
Physics is so much fun! What will they think of next?
*********************
Now, on to your last question: "What's an electron?".
That's the thing you learned about in high school. There may have been
additional properties that physicists were aware of that your high school
textbook didn't bother to mention (or your instructor decided not to
cover), but you're probably aware of them by now.
Just like we thought of light as a wave in the 19th century and then, early
in the 20th century, discovered it could also behave like a particle, so we
thought of the electron as a particle and then discovered that it too could
behave like a wave. But you know that by now.
The fact that there are situations where both could be - HAD to be - at two
different places at the same time (the double slit experiments) was novel.
But that was a matter of discussion 50 years ago and you're probably aware
of this too.
*********************
Over the course of the last century, the discovery of the relativistic
properties of the macroscopic universe and the quantum nature of the
microscopic that followed soon thereafter changed significantly the way
physicists thought about themselves and the world they lived in. The
changes have been revolutionary and we are still trying to figure out how
many of these new ideas fit into the scheme of things.
Best regards,
ron
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