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Watsisname
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11 Feb 2017 06:54

Not exceptionally visible -- just a dim and diffuse glow in all directions.  The density of atoms in a nebula is really small, and the intensity of the light isn't really enough for our eyes to see the color either.  I think they would look more impressive from afar and with sensitive cameras/optics. :)
 
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13 Feb 2017 09:00

Watsisname, so what you see in a nebula in SE is a lie? Also someone asked about the nebula with the most absolute magnitude, NGC 604(you know, that gargantuan pink blob with a diameter of over 1000 light years in the Triangulum galaxy) is probably the most luminous nebula, as SE says it has a absolute magnitude of -12.68, and Wikipedia says -13.8 absolute magnitude. Wikipedia also says that if it was as far from Earth as the Orion Nebula is, it would outshine Venus.
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13 Feb 2017 15:25

Only as much as a lie as the bright and colorful astrophotographs of nebulae.  That is, it's what you would see if your eyes were as big as dinner plates, and could integrate all the light for several minutes instead of refreshing many times per second.  SE's rendering isn't so much simulating your eyeball as a camera with variable sensitivity.

Xoran wrote:
Source of the post NGC 604(you know, that gargantuan pink blob with a diameter of over 1000 light years in the Triangulum galaxy) is probably the most luminous nebula,

For extragalactic nebulae we can resolve, that's probably a good bet for the most luminous.  But figures like "as bright as Venus" at some distance can be deceiving.  It's so luminous because it's so big.  If it were the same distance as the Orion Nebula and we assume it's 1000LY in diameter, it would cover a huge fraction of the sky -- thousands of square degrees.  What's the surface brightness of something the magnitude of Venus spread over thousands of square degrees?  Millions of times fainter.  On average it would be at least 20 magnitudes per square arcsecond, which is a few magnitudes dimmer than the brightest portion of the Orion Nebula.  You would barely even notice it in the sky.  (Though an all-sky deep exposure would certainly be amazing).

I think this is a good demonstration of how diffuse nebulae really are.  To the eye they aren't very impressive up close.
 
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13 Feb 2017 17:59

What would a "garbage" planet look like, as seen from space?

Like, if we were to stop all recycling and stop all safety for disposal of acidic and radioactive waste forever and just threw away everything into landfills and the seas until we ran out of stuff to consume, how much trash would pile up globally and what might Earth look like from space after everything is dead from all the waste? And would trash piles be big enough to see from space?
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16 Feb 2017 00:42

This question would take some researching.  We'll have to know how much trash we make annually, plus the amount recycled (metals, plastics, glass, paper, etc), and how long the supplies will last for the non-renewables at current consumption rates without recycling.

Then the answer will depend on exactly how we choose to throw it all away.  Just make piles on land?  How many piles?  We could imagine a single big pile, or spreading it evenly over every square meter.  What if we dump it all into the ocean?  What if we encapsulate it in pressure and corrosion-resistant containers and sink them along a subduction zone?  There are lots of interesting ways we could choose to visualize it.

"Visible from space" is also open to interpretation.  You might be surprised how easy it is to see things from space -- it isn't very far away.  Some of the larger landfills are already visible by eye from low orbit if you know where to look.
 
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16 Feb 2017 14:06

Good Morning/Evening! Perhaps someone could help tie up some loose thoughts I have.... ;)

The force of gravity is directly proportional to the mass of one object times the mass of the other, and inversely proportional to the square of the distance between them.

If you square the time it takes a planet to go around the Sun, that is always proportional to the cube of the planet's average distance from the Sun

The strength of Gravity is inversely proportional to the age of the Universe, or, Gravity decreases in proportion to the age of the Universe. 
G ∝ 1/t
The mass of the Universe is proportional to the square of the Universe's age. 
M ∝ t^2

So, that means in the far, far future objects will not only have higher mass, they will also be more attracted to one another?
And, moments before the heat death of the Universe it will start to contract again.....?

Oh, and if fusion of Hydrogen requires temperatures of about 100 million Kelvin (approximately six times hotter than the Sun's core), how is Helium created? Is it related to Quantum tunneling?
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16 Feb 2017 17:07

Gnargenox wrote:
Source of the post The strength of Gravity is inversely proportional to the age of the Universe, or, Gravity decreases in proportion to the age of the Universe. 

G is a universal constant -- it does not depend on time.  (If it did then we would need corrections to the Friedmann equations, and there would be obvious observational implications).  The mass of a sufficiently large comoving volume of space is also constant.
Gnargenox wrote:
Source of the post And, moments before the heat death of the Universe it will start to contract again.....?


In the Lambda-CDM model, the cosmological constant will eventually dominate over the radiation pressure and mass density, and the size of the universe (the scale factor) will grow as an exponential with time.  There's never a contraction phase.

Gnargenox wrote:
Source of the post Oh, and if fusion of Hydrogen requires temperatures of about 100 million Kelvin (approximately six times hotter than the Sun's core), how is Helium created? Is it related to Quantum tunneling?

Ah, are you getting 100 million Kelvin from a classical calculation, or are you basing that from typical conditions in fusion experiments in the lab?  Fusion thresholds depend on both temperature and density, so we need higher temperatures in the lab than in the center of stars.  In stars like the Sun it occurs around 13 million K.  Classically, you would also predict no fusion, but in reality the wave function extends beyond the Coulomb barrier and so there is a small chance that the fusion does occur (this is the tunneling effect as you intuited).  It's a fairly low reaction rate even inside the core of the sun (if you calculate number of reactions per unit volume per unit time, it's surprisingly small).
 
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16 Feb 2017 19:34

Well, I got that from Paul Dirac's large numbers hypothesis. I've definitely heard taht if Gravity wasn't constant there would be a violation of the law of conservation of energy (Noether theorem), but Dirac had an idea that introduced into the Einstein field equations a gauge function β that describes the structure of space-time in terms of a ratio of gravitational and electromagnetic units. I have no idea what that means, maybe he was channeling mystics.

I thought, though, since we are only measuring time right now, that it would be similar to the idea that we wouldn't know the difference between Gravity and Centrifugal force if we were stuck in a box. How could we really know time was not different at ... another time... Also evidence for time variability of the fine structure constant based on observation of quasars was noted a few years ago.

I've also wondered if Planck's Constant was different at different ages of the Universe. It is part of Heisenberg's uncertainty principle but is not a part of the Transactional Interpretation of QM, an atemporal interpretation, which has no collapse of the wavefunction dependent on observations, as stated in the Copenhagen Interpretation.

All this just makes me wonder what exactly are all these unchangeable constants based on? Time, Mass, Distance? What is really the most fundamental thing we can truly say is constant and always measurable.

-

Yes, I was thinking about temperatures in labs. Ah, so the tunneling is not really where most of the Helium come from, although some does. It is simply the huge pressures that over come the electric repulsion of protons? Darn, I was hoping for spontaneous false vacuum decay to somehow start right inside our own Sun... LOLOL


I can not tell you how valuable your insight, knowledge, and easy to understand way of explaining things is to me! You're my hero :)
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16 Feb 2017 20:47

For fun, here's the basis of quantum tunneling.  Working this out for fusion with a charged particle approaching a nucleus is hard (well, not so much "hard" as time consuming), but I'll demonstrate the simpler case of "a particle in a box", where the box is a region of zero potential energy, and the "walls" have a finite potential which is greater than the kinetic energy of the particle.  Classically, this is a situation where the particle should never escape.  But quantum mechanically, it can escape with some nonzero probability -- it can "tunnel out".  Here's the rigor behind the why:

The time independent Schrödinger equation for the bound particle has the form

[math]

where [math] is the wave function, [math] is the reduced Planck constant, [math] is the mass of the particle, [math] is the potential as a function of position, and [math] is the particle's energy.  

Suppose the region confining the particle has width "L" (from a position x=0 to x=L), with a potential [math], and the walls have potential [math]

Then for the interior of the region, the wave function must satisfy

[math]

(where double-prime is shorthand for second derivative with respect to x).  This is a 2nd order differential equation, and its associated characteristic equation has complex roots:

[math]

Complex roots means the solution is a combination of sine and cosine:

[math]

So for the inside of the "box", the particle's wave function [math] is an oscillation.  In fact, it looks like a standing wave.  This is the wave-particle duality of matter.

A natural question to ask is where the particle actually is.  The wave function does not say!  Instead, it tells us the probability of finding the particle in some region.  Specifically, the probability of finding the particle at any point is proportional to the square of the wave function: [math].  That means the probability of finding the particle is higher near peaks and troughs in the standing wave, and zero at the nodes.  The precise definition is that the probability of finding the particle in any given region of space is equal to the integral of the square of the wave function, or the area under the curve, and the total probability over all the space must be equal to 1 (100% chance of finding the particle if you look everywhere).

Here's an image to help visualize this.  This is the wave function, and the probability, for a particle in a box with an infinite energy barrier.  Notice there are distinct "energy levels": n=1, n=2, and so forth.  The energy of the particle in the box is quantized.  Each energy level is also associated with a different length of standing wave.

Image


But this image is for an infinite energy barrier, so that the wave function is zero outside the box.  What if the barrier is not infinite?

For the region outside, we have U=U0, so the characteristic equation is

[math]

In this case the solution is [math]

Because the total probability must be 1, [math] must be zero to the right of the box(otherwise [math] will become infinite), and similarly [math] must be zero to the left of the box.  

So on either side of the box, the wave function is a simple decaying exponential [math].  And the image looks like this:

Image

Outside the box, the wave function decays by a fraction of 1/e for every distance [math]  This is often called the "penetration depth".

The penetration depth is generally an extremely small distance.  If we consider an electron with an energy of 100eV, bound within a potential of 200eV, then the penetration depth is just 1.95x10-11 meters!  But if the width of the barrier is comparable to that distance, then the particle can tunnel through, even though the energy of the barrier is greater than the energy of the particle!  To calculate exactly how probable, we need to determine the coefficients of the wave function (these are found by solving a "boundary condition problem", using the fact that the wave function must be continuous at the wall), and then compute the probability for the region outside the barrier.

This is rather tedious to work out by hand, but it can be done very quickly on a computer.  In fact, the hyperphysics website has a page which will do it for you:

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/barr.html

So that's quantum tunneling in a nutshell.  As is par for the course wherever quantum mechanics is involved, it's pretty crazy!

edit: fixed a factor of 2 error in depth calculation
 
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16 Feb 2017 21:43

Gnargenox wrote:
Source of the post Dirac had an idea that introduced into the Einstein field equations a gauge function β that describes the structure of space-time in terms of a ratio of gravitational and electromagnetic units. I have no idea what that means, maybe he was channeling mystics.

Hahaha. :)  I don't know a whole lot about it -- it's well beyond my paygrade -- but I can say that Dirac and others have tried to reformulate general relativity in such ways (there are actually quite a few different GR formalisms), and they receive mixed review.  Dirac's approach is at best incomplete.  If you're interested in further reading material I can see about digging some up.

So, how do we know time wasn't different at other... times?  Actually, we do know that it is different!  By which I mean that the flow of time changes as the universe expands. That's a sort of sloppy way of saying that light from distant events is redshifted by the expansion of space during its transit (a general relativistic effect), so that we see distant events take longer.  And this is the key to measuring how time is or is not variable.  If it is variable, then we will see the same physics play out differently at different redshifts.  This will affect the time-dilation vs. redshift relationship of type Ia supernovae, for example.


Gnargenox wrote:
Source of the post Also evidence for time variability of the fine structure constant based on observation of quasars was noted a few years ago.

Yeah, I recall that too.  If it's true then it's really interesting, and could have implications for the Anthropic Principle (maybe parameters of the universe vary with time and/or space), but if I recall correctly the measured variation was very small, depended on direction, and not convincing within the limits of uncertainty and other factors that could affect the measurement.  I could be wrong -- I'd have to find the paper again.
 
Gnargenox wrote:
Source of the post All this just makes me wonder what exactly are all these unchangeable constants based on? Time, Mass, Distance? What is really the most fundamental thing we can truly say is constant and always measurable.

Seems to be the constants themselves.  They have no derivation -- they can only be found by result of measurement.  Planck's constant was an amazing discovery when you think about it -- no way to derive it from first principles, but Planck stumbled on it exactly when considering how quantization could explain the behavior of blackbody radiation.  
Even the Schrödinger equation itself has no complete derivation -- it's exact form must be set by the result of experiment.


Gnargenox wrote:
Source of the post Yes, I was thinking about temperatures in labs. Ah, so the tunneling is not really where most of the Helium come from, although some does. It is simply the huge pressures that over come the electric repulsion of protons? Darn, I was hoping for spontaneous false vacuum decay to somehow start right inside our own Sun... LOLOL


Oh, the tunneling is important for virtually all of them.  The nuclei have a distribution of speeds, and that distribution is low enough that classically, the probability of fusion occuring is pretty much nil (like 1 in 10>100).  With tunneling its vastly more likely (but still pretty rare -- more like 1 in 1031).

Thanks for the feedback; I really enjoy answering questions and love seeing all the enthusiasm for science and learning. :)
 
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16 Feb 2017 22:49

I will pour over this for hours!!! Thanks again!
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21 Feb 2017 18:51

Watsisname wrote:
This question would take some researching.  We'll have to know how much trash we make annually, plus the amount recycled (metals, plastics, glass, paper, etc), and how long the supplies will last for the non-renewables at current consumption rates without recycling.

Then the answer will depend on exactly how we choose to throw it all away.  Just make piles on land?  How many piles?  We could imagine a single big pile, or spreading it evenly over every square meter.  What if we dump it all into the ocean?  What if we encapsulate it in pressure and corrosion-resistant containers and sink them along a subduction zone?  There are lots of interesting ways we could choose to visualize it.

"Visible from space" is also open to interpretation.  You might be surprised how easy it is to see things from space -- it isn't very far away.  Some of the larger landfills are already visible by eye from low orbit if you know where to look.

I did some googling, and we currently pump out 2.12 billion tons a year. My scenario assumes we just litter everything everywhere, so after 167 years, for example, we would have 355 billion tons.

However, Im having issues with my math. According to one website, 2.6 trillion pounds of trash currently exist. However when I convert it to tons, it is 1,179,340,162 tons, or almost 1.18 billion. Is this right? I mean, if we put out 2.12 billion tons per year, shouldnt the figure for existing trash be much greater?
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22 Feb 2017 04:48

Clearly one of these two values are necessarily wrong. Eventually there might be a misunderstanding. :)

Anyway, now you got me an idea for eliminating all this thrash: Could we put it in the earth's nucleus? No no no, wait. Let's put it this way: Could we reach the earth's nucleus to release this thrash without being squashed by high pressures and without causing structural damage to the planet (creating a volcano or new fractures in tectonics)?

I'm going to answer myself: No, not now at least, but it is an interesting idea indeed. Even because throwing it at the sun requires too much energy (because you need to cancel earth's motion around the sun) and putting it in the ground/under the sea is as easy as dangerous for the environment.
The universe is not required to be in perfect harmony with human ambition.

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22 Feb 2017 16:20

Actually, I'm asking this question because of a personal creative world building project; the setting is in the future and the Earth was abandoned after too much trash killed the environment. Googling around a bit, I learned that peak trash production may be up to 11 million tons per day by 2100 or so. In my setting, that amounts to 670.505 billion tons of accumulated trash build up by 2184, the year the biosphere collapses.

As for my other numbers in my previous post, maybe the mismatch is because current recycling efforts weren't taken into account? Some quick googling revealed a 30% to 34% Recycle rate, but that was just for the US. Additionally, i dont know if these numbers include industrial and/or commercial trash, rather than just household trash. Do they?

Anyways, assuming a global trash accumulation of 670.505 billion tons of trash, and if each piece of trash (and drops of liquid of acids) were spread out evenly across the entire surface, for example, would that be noticable from space? Like a change in color of the ground or sea?
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22 Feb 2017 18:22

I have always wondered--we can confirm that a star has planets, right? But have any stars been found not to have any planets? (And does SE know not to generate procedural worlds for them?)
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