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Sequence Page 6
A World of Calculation
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Introduction
Introduction
The story so far: I began with evidence for subatomic particles,
discussed light and the information available in dots, looked at
connections between people and stars, and went on to build some simple
hermetic worlds inside
computers... none of this has been too difficult. I also
considered the
liberation of electrons by light from solids and this obliged me to
review some more involved physics, particularly 'ensemble system'
physics or statistical physics. That was a little harder but also not
too
bad in my view. It was also connected to some questions concerning the
rolling dice of dice.
So far so good and I
think it's time I take on a truly difficult problem. Something
closer to the base of my mountain range of incomprehension. That will
be page 8.
Page 7 will be a medium-hard warmup and page 6 will be an easy
warmup-warmup.
Page 6 is calculations, deriving numbers for questions on scales from
electrons to galaxies.
To Git
Goin'
The physical constants in use here are listed out on this supplemental page.
The first question I want to address is concerned with earth's moon. I
view the moon via reflected sunlight, and in particular a new moon
shows a ghostly but nevertheless illuminated 'dark side', the
side away from the sun. The light source is still sunlight, but this is
sunlight reflected off earth, so it is sometimes called earthshine. Fair enough but I am
part of that reflecting earth that illuminates the moon... so some
component of earthshine is actually reflected off of me. I will call
this robshine.
Now a simple model of the sun's energy production says that a nuclear
reaction (see the proton chain on page
2) produces a single photon that ricochets around inside the
sun for a million years or so before reaching the surface and escaping
as visible light into space. This is an oversimplification but let's
take it at face value (or poetic value). I want
to know the answer to this question: How often does a photon leave the
sun and bounce off of me to
strike the shadow-side of the new moon and from there to subsequently
bounce back into my eye? It has to happen, right? I mean there's the
sun, there's the moon, I'm standing there... it has to happen. But how
often? A million light particles per second? One light particle
every ten thousand years?
More questions:
What is the escape velocity on
the moon?
What is the speed of a free Hydrogen
atom at moon-surface-temperature?
And implications...
If I am standing on the moon can I see spherical curvature at the
horizon?
How much does the galaxy weigh?
How much does our sun weigh?
How many suns fit in a galaxy?
Under <certain conditions> what is the necessary mass of the odd
thing at the center of the galaxy?
At room temperature how fast are the oxygen molecules O2
moving? (and related)
What does relativistic mass contribute to a gas at a given temperature?
What does this imply for very high temperatures?
How many electrons are on this comb that I'm using to pick up this
little scrap of paper?
What is the intrinsic electrostatic energy of a charge ensemble?
How does this compare to gravitational energy?
What is the energy of a paperclip?
How big is an atom of hydrogen? There is a quick-and-luckily-accurate
derivation here.
What is the ground state binding energy?
How big is an electron?
Do electrons have self-dislike?
What is the difference between photon-as-solution-to-Maxwell and
photon-as-quantum-of-energy?
What Next?
What's next is supposed to be a tractable warm-up calculation of
moderate difficulty. I'd like to count photons involved in some
electromagnetic interactions, starting with the deflection of a rolling
metal sphere that passes near a magnet. While counting angels dancing
on pinheads is beyond me, I'm optimistic there are some cases where I
can answer the question
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