The Physics of Baph

That title sounds a bit intimidating.

So, in order to start this off properly, I want you to imagine a star. Size, shape, color, none of that is necessarily important right now. Just think of your basic star.



There we go. That wasn't so hard now, was it? Now, pick a point on its surface. Any point at all; doesn't matter. This will be point A. Now, pick any other point on the surface; again, it doesn't matter (as long as it's not point A). We shall call this point B. Remember these points; I'll come back to them later.

Now, the first and perhaps most important question here: How does one actually observe a star?

The answer to this is deceptively simple: photons from the star go through your pupil and hit the back of your eyeball. Now, whether this is through a telescope or not is not important right now. All that's important is to know the act of observation requires the photon to go through your eye.

Next question: What is a star in the first place? Again, the answer is deceptively simple; a star is merely a ball of plasma undergoing nuclear fusion. Specifics aren't necessarily important at this time.

Now, recall A and B. If you've forgotten them, you have a worse memory than mine; simply choose another two. Now, why should you care about points A and B? Remember, the star you're thinking of is merely a ball of flaming gas. It has no means of communicating between points A and B, telling them both to release a photon of similar amplitude and wavelength at the Earth at the same time. As such, they probably don't.

Now: What is a photon? For this, we need two definitions: First, a photon is a wave packet with specific wavelength and amplitude that behaves like a particle in interaction, sort of. Second, a photon is a Boson, which fits with the second half of the first definition I guess. Why does the second definition matter? Because a Boson behaves in a very peculiar manner.

If you're familiar with protons and electrons, you might know they're part of a group of particles known as Fermions. A fermion, according to the Pauli Exclusion Principle, cannot occupy the same quantum state as another Fermion. Basically, they cannot have the same attributes as another, ever. This has some neat ramifications in astrophysics, but that's a lecture for another time. Bosons, on the other hand, can not only occupy the same quantum state as others, but actually tend to conform to those around them over time. Now, what does this mean?

This means that, after a significant distance r, a collection of photons released randomly from a single star will become what is known as coherent light - basically, very similar physically to laser light: the longer they are together, the more they trend towards equivalent wavelengths, amplitudes, even spin. For this reason, we can also think of observing a star as having a single wave front (think tidal wave of light, sort of) collect in our eye at a specific time. Again, this has interesting ramifications, but that's exactly what the rest of this "lecture" is about.

Now, let's say for sake of simplicity that a single, spherical wave front is emitted from a star. This sphere expands at the speed of light until it eventually collides with our eye on Earth. Very often, this is only a miniscule fraction of the sphere itself, and that is of moderate importance here; the rest of the importance of it is for another time. Anyway, because the distance r between the star and your eye is very much larger than the aperture of your pupil, it is absolutely safe to simplify the result even further and say that the wave front is actually a plane as opposed to a sphere.

Now, consider Sol, the central gravitational point of our planetary system. Again, this star is much farther away than the size of your pupil, so again it is safe to assume a plane wave front. Even, say, the size of the Earth is small compared to the distance it holds from Sol, so a wave front in relation to the planet can again be assumed planar. What does it mean?

Sol is sufficiently far enough away that photons from it have begun to become coherent by the time they reach Earth, a mere eight minutes or so later. As a result, it can be assumed that most of the photons from the sun have similar quantum states. Now, imagine a single wave front propagating from Sol and reaching Earth. This wave front collides first with the atmosphere closest to it; as the photons pass through, blue is the most common wavelength to be scattered. As it continues colliding with the rest of the atmosphere, going around the sphere of the planet, it has to go through more and more air. The more air it goes through, the more wavelengths get filtered. Red, being longer in wavelength than the other colors, is the last one before the scattering completes, and only occurs as a true red when there's moisture in the air; this is why the sky turns red at night.

So, what about this plane wave front at the location on the surface of the Earth closest to Sol itself? It does what it did to the atmosphere - collide with it. Every surface, every atom, is hit by this wave front. Trees, streets, people, everything. Because most things have a much higher reflection coefficient than transmission, this wave then bounces off these objects at specific wavelengths, depending on what they are. This is why we percieve the world in color.

Now, these reflected waves will not always collide with your pupil, but it tends to be the case that enough of them will that you'll be able to see the object itself. Were it not for the planar nature of the initial wave front, we would not be able to percieve three-space the way we do. If those photons were of the same quantum state they were when they were first emitted, who knows how we'd see the world. All sorts of things might have different colors; in fact, we might be colorblind, because there would be no point in being able to dicepher the difference if it were as random as that. Our entire concept of physics, biology, chemistry, and geology might be skewed simply because we evolved without knowing the varying wavelengths of photons, merely their amplitude and number.

That concludes today's "lecture". Any questions?

I was thinking about this last night; the logic is probably horribly incorrect, so if you think there's a problem with it, tell me please.

( Universe: Infinite? )

Q: When a star collapses, I've noticed the result usually has a spiral of material surrounding it and falling towards the center. What is this, and what causes it?

A:
This is known as an accretion disk.

Before a star collapses, it is rotating. There is no argument here; even the slightest rotation is still rotation, and would still have an effect. This rotation introduces several factors to the system, the first important one in this scenario being angular momentum.

As a star collapses, this angular momentum begins to make its effect known. Non-relativistically (we're not going to go into relativistic effects just yet), angular momentum of a particle moving in a circle is defined and can be derived by

L = mvr

where L is angular momentum, m is the mass of the particle in question, v is the objects angular velocity (not important to explain here), and r is the distance of the particle from the center of the circle in which it is traveling. If one were to ponder this, it would be noticed that v and r are inversely proportional; that is, as one decreases, the other must increase to maintain the equation. This is because angular momentum is always conserved.

In other words, as the star collapses, the observed particle is brought closer to the center, and thus must increase in angular velocity to maintain conservation. This causes a spiral pattern in the particle's path.

The next factor in the creation of an accretion disk is something of a misnomer, known as the centrifugal force. This is not a true force, but is acceleration felt due to rotational acceleration. When you travel in a car and take a rather sharp turn rather swiftly, this "force" is felt as your body pressing against the outside edge of the turn; it is what causes particles orbiting a point to want to leave its orbit and continue in a straight line. this is translated, in our scenario, as a flattening of the debris of the star, into a disk shape.

Now, what dictates which direction the disk is oriented relative to the new astral body? Remember that it's still rotating, even as it shrinks; the result of this is known as a tidal effect. An observable example of this is in Earth's oceans, and truely the Earth itself. The Earth is not a perfect sphere; it is instead what is known as a spherical ellipsoid. This basically means that there's a bulge in the planet around its equator, almost as though it were being squished. This bulge is due to the planet's tidal effects. These same effects affect the gravitational field around the body, aligning it in the same manner. This causes the accretion disk to eventually line up with the body's rotational equator.


For those interested, this tidal effect can be determined by

F = 2GMmr/(R^3)

where F is the tidal "force", G is the Gravitational constant, M is the mass of the object in rotation, m is the mass of the object on which the force acts, R is the distance between the two bodies, and r << R is the distance from the reference body's center along the axis.

Because the material in the disk is viscous, it produces quite a bit of friction. This friction generates obscene amounts of heat and saps orbital momentum, causing the material to spiral in towards the center until it collides with the surface of the object.

Welcome. You appear to have stumbled upon this journal quite accidentally, as there is no other logical reason. Unless you genuinely love physics, namely astrophysics, to such an extent that you would actually attempt to find this place.

My name is Baphijmm. I shall be your guide into the deepest, darkest recesses of modern astrophysics. Sit back and enjoy the ride, but take heed, it shall get quite bumpy along the way.