Avoid the temptation of using more than one mass.  It only leads to confusion and potentially wrong predictions.  It is much more simple to say that there is only one mass, and it does not vary with speed.

I'll want to use a little math to explain some of this, but will place emphasis on conceptual understanding.

The pdf actually has a really good quote about this in the intro, and its motivation is to try to unteach this common notion of mass depending on speed.  It tries to convince you that using "rest mass" and "relativistic mass" are unnecessary.  It even argues that "rest mass" itself is a lousy term because that suggests there is some other mass related to motion.  I agree.

This famous equation and the concept of mass increasing with velocity indoctrinate teenagers through the popular science literature, and through college text-books. According to Einstein, "common sense is a collection of prejudices acquired by age eighteen. "It is very difficult to get rid of this "common sense" later: "better untaught than ill taught." As a result one can find the term "rest mass" even in serious professional physics journals. One of the aims of this book is to help the reader to get out of the habit of using this term.

Another useful quote:

In the modem language of relativity theory there is only one mass, the Newtonian mass m, which does not vary with velocity~ hence the famous formula E = mc² has to be taken with a large grain of salt.

 
Here I would disagree with the "Newtonian mass" because that raises more questions like what is Newtonian mass, and what's a non-Newtonian mass?  Ignore it.  The important part is it does not depend on speed.  I'll also disagree with saying that E=mc² has to be taken with salt.  The formula is right!  The catch is that you have to know what the m and the E mean.  This E is not the kinetic energy, or the total energy.  It is the internal energy, and that is why it does not depend on speed.

What does depend on speed is the total energy, which is mc² times [tex]\gamma[/tex] ("gamma").  Gamma is what captures the essence of relative motion in relativity.  At slow speeds it is very close to 1.  At very fast speeds, approaching the speed of light, it goes to infinity.

We can also say that E=mc² is actually a part of a more general formula, [tex]E^2 = (mc^2)^2 + (pc)^2[/tex].  Here E is the total energy, and again mc² is the internal energy.  p is the momentum.  This explains why massless particles like photons have momentum.  The formula p=mv that is taught early on in physics is Newtonian.  In relativity, massless particles have momentum p=E/c.



So anyway, what the heck is mass?

Mass is a measure of the internal energy of an object.  It is the sum of its parts, plus an energy associated with how those parts are bound together.  Every fundamental particle has an established mass.  A proton has a mass of 1.67x10^-27kg.  Always.

That the mass is associated with the energy involved in binding the parts together is very interesting, and is the thrust of E=mc².  It means for example that a stretched spring literally weighs more than it does when relaxed, because there is an additional internal energy associated with being stretched.  It is also the basis for how the Sun emits energy by fusing protons together.  When you combine the protons, they reach a lower energy state than if the protons were separated.  So the internal energy is little bit less than the sum of the parts, and the difference was emitted as radiant energy when they fused.  Hence, sunlight!  

Finally, because the value of c is big, and squaring it makes it even bigger, the relationship says that a tiny change in the mass represents a huge change in the internal energy.  E=mc² describes mass-energy equivalence, but it is the rest-mass and internal energy that are equivalent.

All good and well, but then why does kinetic energy not change the mass?  We could say that it does by defining a relativistic mass, but again, avoid the temptation!  That would be a definition of mass that depends on frame of reference.  Instead, notice that the mass measured in the object's own frame never depends on how fast it is moving.  This makes it easy to define, easy to measure, and everyone everywhere can quickly determine the value and agree on it.  It captures the properties of the object itself, and not situational circumstances like how fast the observer is moving which do not affect those properties!

Want to determine the mass of something moving fast?  Easy!  Let it hit something and come to a stop.  Then its kinetic energy is reduced to zero in your frame, and must have been converted to something else.  The total energy reduced from [tex]\gamma mc^2[/tex] to [tex]mc^2[/tex].  The difference is [tex](\gamma - 1)mc^2[/tex].  That's how kinetic energy is defined in relativity!  (The Newtonian formula, [tex]KE=\frac{1}{2}mv^2[/tex], is wrong at high speeds.)

Notice the mass did not change when we stopped it.  It was m before, and it is the same m after.


An outstanding question at this point might be why we speak of the masses of particles increasing in particle accelerators.  By observation, the products of colliding two relativistic particles can have greater mass than the components.  Doesn't that mean the high velocity of the components increased their masses?  The answer is no!  When they collide (let's say perfectly inelastically), their kinetic energy drops to zero.  This converts it, very briefly, to internal energy.  That internal energy is then what provides the mass for the resultant collision products by E=mc².

Ooo kay.. 3 pages into that and I realize I need to read this first: The cause of Gravity (& other Strong Force mumbo jumbo)

Ah, I actually advise skipping that one entirely.  The first link you found is a lot better and will help you reach a good understanding.

The problem with the latter is that although it might sound good, it is actually based on a number of misconceptions, and its argumentation is fairly hand-wavy.  Its references are mostly popular articles and books but not very much academic publications in gravitation or cosmology.

In fact one of the central ideas behind the formulation of general relativity is in providing a tensorial description of how mass energy leads to space-time curvature.  So this new theory has a flawed motivation -- you do not need to look to the strong force to understand where gravitation comes from.  Then it makes a number of qualitative or conceptual claims but fails to show rigorously how they follow.  The claim about the sources of gravitational braking on the early expansion of the universe has some serious issues.

So, yeah, if you want to to get a better understanding of relativity (special or general) and E=mc², there are better resources available.

Cool, I think. I was just heading down the path of thinking that the strong force holding gluons in some sort of Chinese finger trap tube & the vibrations or frequencies of them in this tube are adding energy to the atom, and hence adding the majority of the mass to atoms.

The strong force does not hold gluons. The strong force is the gluons.  They are the force carriers, massless and travelling at the speed of light, and their exchange is what binds the quarks together in baryons (this is also called the color force, and the strong force is in the context of how this binds protons and neutrons together).  Most of the mass of the baryons is in the binding energy of the quarks.  

It's analogous to how you can treat the electromagnetic interaction as an exchange of photons.  But rarely do you bother thinking about what virtual photons are doing when modeling the energy of a proton and electron bound in an atom.  Much easier to use the potential -- the relationship between change in energy with a change in separation.

A useful model for the binding energy of quarks is to think of them being inside an elastic bag, or attached by a spring (but one with a more sensitive relationship than Hooke's Law), and the energy involved in pulling them apart rapidly leads to pair production.

Incidentally, this is one of my favorite examples of mass-energy equivalence.  By trying to pull quarks apart, you are adding energy to increase their internal energy, but this grows so quickly with separation that it ends up producing new pairs of quarks!

The interstellar medium is extremely tenuous, with the large gas clouds you'd typically see across the sky appearing invisible while the observer is in them. What I find odd though is how some regions of the Interstellar medium become extremely (relatively) dense to the point it's visible (such as the Orion Nebula complex) with no slow transition of the gas steadily becoming visible. Why is that?

Also the closer you get to the sun the more blinding it becomes, right? I don't know why it isn't like that in SE.

Are these new quarks "borrowed" from somewhere? Are they simply NEW particles or bundles of energy? (Turning energy into matter was a bigger deal I thought). Are they there only because you are peaking around the corner into another dimension, and their coming and going is something we can only see some of the time?

Mass can be stated simply as the amount of gluon exchanges?

I've also heard of mass being expressed simply as time.

I love Hyperphysics pages, now I need find out what jets of mesons are all about .. haha.

It's hard to know where to start and what is constant. I don't even know what all the factors are in what I am trying to learn lol. Mass, Time, Vibrations, Frequencies, Compton wavelengths, Spin, Color, Gravitational Forces (an illusion?), Electromagnetic Forces, & Strong and Weak Nuclear Forces, Multipass (5th Element movie reference), Yukawa potential, and new force-carrying photons only 30 times as heavy as electrons... I just don't know what to unlearn and where to begin.

I also have a fear of accepting Planck's length as truly constant, since the beginning of time. (Red shift of Quasars)

You truly are the best resource I've ever stumbled across! I owe you some chocolate chip cookies, sugar free if you'd like.

What I find odd though is how some regions of the Interstellar medium become extremely (relatively) dense to the point it's visible (such as the Orion Nebula complex) with no slow transition of the gas steadily becoming visible. Why is that?

There are a couple of reasons.  First is that the gas really is becoming dense quite quickly (astronomically speaking), because these were large clouds of gas that have (are) collapsing gravitationally to produce stars.  The density increases dramatically towards the center of the cloud where the stars are forming.

The second has to do with what makes the gas luminous.  By itself it does not glow visibly.  The atoms must be excited or even ionized. Then when the electrons jump back down to lower energy levels they emit photons.  The transitions which produce visible light are the Balmer Series, which is what gives the characteristic pink color of emission nebulae.  (The transition from the 3rd to the 2nd level is called hydrogen-alpha, and makes the distinct red color seen in the image at left.  Filters that allow only this color of light to get through are very popular in astrophotgraphy).

For these transitions to occur the electrons must absorb photons of sufficient energy, and typically this means ultraviolet light.  So we most often see this when we're looking at a star formation region, and some of them are visible to the eye like Orion.  Even so, being inside the Orion nebula would still seem a very empty place -- more like a diffuse and faintly luminous fog all around.  You would barely notice it.

Another aspect of the interstellar medium is dust, which both absorbs and reflects light. The reflected light is typically blueish for similar reasons that the sky is blue, and this is what makes reflection nebulae.  The light that goes through is dimmed and reddened, so when you look through a dense cloud of dust it may appear black, like a void in the field of stars.  You can see dust lanes across the nebulae at left, and as the disk in the galaxy at right.  Even with the naked eye from a very dark observing site, you can see the dust lanes in the Milky Way.  Or better yet in a photograph:


Most of these dust clouds are definitely not dense or sharply defined, and it is visible because we're looking through very long distances of it.  But sometimes these clouds of dust can be so sharply defined that it is quite remarkable.  For example, with Bok Globules:



These are so sharp and retain their shape because the dust is very cold, and with infrared observations (that penetrate the dust) we can see they are also often collapsing and forming stars inside.  Another aspect of their sharp definition may be due to them being sculpted and eroded away by the pressure of the surrounding light, as with the Pillars of Creation.

Also the closer you get to the sun the more blinding it becomes, right? I don't know why it isn't like that in SE.

The Sun gets more blinding as you get closer because its disk appears larger and it forms a larger image on your retina.  Or you can say that more light altogether is entering your eye.  But the surface of that disk itself is always the same brightness -- the same amount of light per unit area.  Space Engine correctly shows this.

The Sun gets more blinding as you get closer because its disk appears larger and it forms a larger image on your retina.  Or you can say that more light altogether is entering your eye.  But the surface of that disk itself is always the same brightness -- the same amount of light per unit area.  Space Engine correctly shows this.

So...that means the closer you get to the sun, the more visible it's circumference and surface would be?

Are these new quarks "borrowed" from somewhere?

They are the physical manifestation of ethereal energy transmitted through parallel dimensions.

No, not really. The notion that we're making new quarks "out of nothing" is indeed very strange.  But when you think of it in the context of quantum field theory, it makes a lot more sense.  Quantum field theory says that every particle is an excitation of a field.  When you try to separate two quarks from each other, you have to put energy into them, similarly to how you must input energy to stretch a spring.  This energy goes into exciting the gluon field, and when you separate them enough, the excitation of the field is so strong that it produces a pair of quarks in a process called pair production.  

Conceptually, think of the field as a sea, and a particle is a ripple on that sea (it does not necessarily need to move or spread out like a ripple).  If you poke that sea hard enough, you can create new particles.  The mass of the particles was "borrowed" from the energy of your poking at it.

Pair production is weird, but also not unique to quarks.  You can create an electron and positron pair "out of nothing" by sufficient excitation of the electromagnetic field.  But conservation of energy and momentum always applies, and in order for them to be conserved the way this production occurs is by shooting a high energy photon near an atomic nucleus.  The energy of the photon is converted to the mass and kinetic energy of the electron/positron pair, and the (very small) recoil of the nucleus allows the momentum to be conserved.  (The nucleus is required to conserve momentum because we can always choose a frame of reference where the electron and positron have opposite velocities and thus the final momentum is zero, but the photon has nonzero momentum.  The nucleus can take the difference.)

...yeah, pair production is weird.

Mass can be stated simply as the amount of gluon exchanges?

This would fail to explain the mass of leptons like the electron, which are massive but experience no strong interaction.  But for the sake of understanding hadron (combinations of quarks) masses, basically yes.  The energy associated with all the gluons acting to bind the particles together is a very big part of their mass.  You can think of it as the gluon exchanges, or you can also think of it as the potential energy of the quark distribution.  They're the same idea expressed with a different physical model.

I've also heard of mass being expressed simply as time.

Mass endows particles with the ability to experience time, but to say mass is time is a bit wrong.  Actually there's an awesome PBS Space-Time episode about this, though it can be a lot to digest!

[youtube]fHRqibyNMpw[/youtube]

I love Hyperphysics pages, now I need find out what jets of mesons are all about .. haha.

Happens when you try to tear quarks apart with too much violence.  A important experiment in particle physics is to strike the nucleus with very high energy electrons.  A principle of quantum mechanics (the de Broglie wavelength) says that the "size" of a particle is inversely related to its energy.  So a high energy electron has a very small cross section, much smaller than the nucleus, and in these "deep inelastic scattering" experiments this allows them to probe the structure of the nucleus and demonstrate the existence of quarks. 

When the electron strikes the nucleus, it imparts so much energy that you would think it would tear the quarks apart.  But as we just described, quarks hate being separated, and that energy goes into making new quarks.  More specifically, quark-antiquark pairs, or "mesons", which are unstable.

In other words, this is how we know you can't separate (and isolate) quarks.  You just get more quarks!

I also have a fear of accepting Planck's length as truly constant, since the beginning of time. (Red shift of Quasars)

I'm unfamiliar with this!  You'll have to tell me more.

(I'm pretty sure everything involving redshift of quasars is just due to cosmic expansion, but maybe there's something anomalous I'm unaware of.  But even then, taking it as evidence of variation in Planck's constant is difficult, because if it varied that much by the time quasars were around, then it would really screw up the physics of the early universe, like recombination and especially nucleosynthesis.)

You truly are the best resource I've ever stumbled across!

Thanks!

So...that means the closer you get to the sun, the more visible it's circumference and surface would be?

If your eyes can adapt indefinitely like a camera, yeah, but in reality they'd be cooked.

So...that means the closer you get to the sun, the more visible it's circumference and surface would be?

If your eyes can adapt indefinitely like a camera, yeah, but in reality they'd be cooked.

But they can't adapt indefinitely in lieu of being destroyed  by the sun's intense heat.
So how would it look like to the human eye?

Also wouldn't the light coming from faraway stars twinkle or something similar due to diffraction in the cornea?
(Observer is not in the atmosphere).

So how would it look like to the human eye?

Like a seething white orb of painful stimulation, probably with an involuntary blinking or "look away" reaction, followed by afterimages and possibly retinal damage.  If you struggle to see details like sunspots you will be blind before you see them.

Also wouldn't the light coming from faraway stars twinkle or something similar due to diffraction in the cornea?

No, they would be crisp and steady.  Twinkling of starlight in the atmosphere occurs because of the rays travelling through pockets of air with different densities, which over the long path from sky to ground not only spreads it out, but also spreads it out in different directions at different times, hence the twinkling.

Diffraction does occur in your eyes, but it instead of causing twinkling it causes effects like haloes and color artifacts.
You can test this by looking at stars under very calm skies (clear does not imply calm).  Under calm skies the stars will be steady!  Amateur astronomers will actually know to use this as a sign of when they can get very crisp images of the planets.  When the stars do twinkle a lot, the planets will look like they are behind a veil of shimmering water or heat haze.

So how would it look like to the human eye?

Like a seething white orb of painful stimulation, probably with an involuntary blinking or "look away" reaction, followed by afterimages and possibly retinal damage.  If you struggle to see details like sunspots you will be blind before you see them.

Also wouldn't the light coming from faraway stars twinkle or something similar due to diffraction in the cornea?

No, they would be crisp and steady.  Twinkling of starlight in the atmosphere occurs because of the rays travelling pockets of air with different densities, which over the long path from sky to ground not only spreads it out, but also spreads it out in different directions at different times, hence the twinkling.

Diffraction does occur in your eyes, but it instead of causing twinkling it causes effects like haloes and color artifacts.
You can test this by looking at stars under very calm skies (clear does not imply calm).  Under calm skies the stars will be steady!  Amateur astronomers will actually know to use this as a sign of when they can get very crisp images of the planets.  When the stars do twinkle a lot, the planets will look like they are behind a veil of shimmering water or heat haze.

Thanks. I just wondering because to me, stars sprites in SE don't look very realistic compared to images like these. Though I can't quite put my finger on it. (Disregard any lense diffraction spikes).

Yeah, in the next version you will be able to customize star sprite appearance more.  It is possible to get closer to either a photo-realistic "astrophotography" look like in those images, or something more like what the eye sees:

Also the closer you get to the sun the more blinding it becomes, right?

Light intensity follows the inverse square law.  So if you halve the distance, the intensity goes up by the factor of four.  Just like area has a squared relationship with size.  So, half the distance gives twice the size and four times the area.  Consider the full moon against the dark sky.  If you approach it, it will be increasingly easier to read in its light, but the surface wont become brighter.  It's just more of it.