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?

Yeah, that would definitely be noticeable.  It would amount to about 1 kilogram of trash for every square meter of surface area.  If it is only spread over land area, then it is more like 4 kilograms per square meter.  

Needless to say it's totally implausible for trash to be spread evenly like that, but we can use this as a helpful way to visualize how much trash it is.  Another good visualization is to consider it in a single pile and ask how tall and wide that would be, or spread evenly over a smaller area and ask how deep it would be.

To do that we'll need to come up with some average density.  There are a wide variety of trash densities, and how they get compacted is also important.  But for order of magnitude estimates, let's take it to be fairly highly compacted at 1000kg/m³.  That means 670.505 billion tons would take a volume of around 600 cubic kilometers!  Let's come up with some visualizations of that:

-It would bury all of Earth's surface (land and sea) to a depth of 1mm.  (Is that impressive?  I can't really tell.)
-It would bury the state of Texas to almost a meter.  (Pretty impressive).
-It would bury everything within the former 10x10 mile "diamond" border of Washington DC under more than a mile of trash (very impressive and probably an improvement for the city).

What if it were a conical pile?  Suppose it had an angle of repose of 30°.  Then it would be over 8km high, and 30km wide at its base.  It would dwarf mountains like Kilimanjaro or Everest (but not Hawaii, as measured from the sea floor).

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)?

Not likely (temperatures are comparable to surface of the Sun and pressures of hundreds of gigapascals [over a million atmospheres]).  Even if you could make a hole, you could not keep it open.  Even if you could keep it open (perhaps with some futuristic metamaterials), it still seems like a wildly inefficient way to deal with the problem.  

A lot of people entertain the idea of shooting it into the Sun, but as you pointed out it's a pretty poor choice considering the delta-v requirement.  Sending it into Jupiter actually seems like a better idea -- the velocity at atmospheric entry would vaporize it -- but it's still a bad option when you consider the cost, and potential consequences of error (e.g. contaminating other solar system bodies).

The best way to solve the waste problem is simply to be smarter about how we generate, recover, and convert waste.  We can do a lot better with how we recycle used materials, break down others through chemistry (sometimes even using clever biochemistry to deal with toxic stuff and heavy metals), and reduce our reliance on materials that are neither reusable nor degradable.

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?)

Just in case nobody saw this

Ow, Hornblower, this is a bit counterintuitive. I guess we can't be really sure of this absence until the ultimate generation of instruments or new advanced observation techniques kicks in, but in case, we just need to place the star in one of the catalogs with a "NoPlanets true" parameter.

(And does SE know not to generate procedural worlds for them?)

You can mark it in the catalog file, that part I can answer.

Just in case nobody saw this

Yeah, we cannot yet demonstrate an absence of planets.  A star could have a planetary system whose orbits are "face-on" to us, in which case both the radial velocity method and transit method would see nothing.  Those planets could instead be found by direct imaging, but that only works if they are big and orbit far from the star -- otherwise they are lost in the glare.  

So to prove that a star does not have planets, we must be able to directly image even small planets very close to their stars.

I figured. But how about if there is any star that has no confirmed exoplanets, but clearly no massive object. Would SE know not to generate high mass Ice and Gas Giants?

As Watsisname says, when the planet is close to the star, it can not be discovered. With our previous methods. Therefore, we can not say for sure that a star has no planets.

Nevertheless, I would advocate the implementation of a parameter like 'NoGiants true' so that planet systems can be generated without gas and ice giants.

What would happen is space-time distorted to the point an object was inside it's self? Fusion? Blackhole? 

What a fascinating question.  There are several ways to think about how this would work (in theory, probably not so much in reality), and they're all weird.

The way I'm thinking about it is to take a particular slice of the space-time at a moment in time (in other words, one observer's notion of the where everything is at particular moment of "now"), and finding an object which contains a smaller copy of itself, and the two are actually the same object.  Like a hollow sphere which contains another smaller hollow sphere inside, and they are the same sphere.

To make sense of how that would work, we can use a space-time diagram.  But before we do that, let's use a space-time diagram to explore a simpler scenario, so that we get comfortable working with them.  In this diagram and in all to follow, space is the horizontal axis, and time is the vertical axis:



We haven't messed up the space-time very much here yet.  Nothing is going inside of itself.  There is an object (perhaps a sphere) centered around x=0, and two circles are drawn in to represent the location of its edges.  An open circle on the right side, and a filled circle on the left. 

There are also some vertical-ish lines going through the diagram, which represent "world lines".  You can think of such a line as the "history" of an object -- where it is in space throughout time.

Finally, there are some cones drawn on the lines.  These are "light cones", which represent where an object is allowed to move.  The edges of the cones are 45° angles, and are defined by the speed of light.  Meaning, if you are at that point in the space-time, then to move along the edge of the cone, you must move at the speed of light.  Since nothing can go faster than the speed of light, you can only move in the direction that your light cone is facing.  Basically, the cone indicates the direction in which time is flowing.

As time increases, we see that world lines converge toward x=0.  The light cones also turn to face inward, which represents that the space-time is getting curved.  Gravity is pulling things inward.  This would be exactly like a collapsing star (although here I do not have it collapse completely to a black hole.  If it did then a bunch of the lines would come together at x=0 and we would get a singularity).  

So what's happening to the object represented by the two circles?  It is simply shrinking.  In the future, it is smaller than it was in the past.

OK, now let's make the object not only become smaller, but also be inside of itself.  How would we do it? We'll have to do something pretty crazy to the space-time.  Perhaps something like this:



What is happening here?  

The space-time is incredibly distorted.  It is so distorted that some world-lines are bent all the way around into closed loops.  These are "closed time-like curves" (CTCs).  If you lived on a CTC, you would travel to your own past!  These kinds of curves exist in some metrics of space-time (such as near ring singularities in a rotating black hole, or in Gödel's metric describing a rotating universe.)

In this case, we have two regions of CTCs which curve in opposite directions.  Kind of like a torus, except this is a crazy 4-dimensional torus.  It causes the edges of the object to collapse, then move backwards through time, expand again, and then meet back up with itself.  In a certain sense, there are times where it exists twice, one inside of the other.  Weird!  

There are also three special points in this diagram.  One is in the center of the object at x=0.  Space-time is behaving very oddly near this point:



Basically we have a point where time has a really difficult time figuring out which way to flow.  It is a singularity, but a special kind of singularity and completely unlike what exists in a black hole (a typical gravitational singularity has all paths and light cones flowing into that point).  Here, the paths turn very sharply in different directions.  Mathematically this is a type of saddle point.  The sharp turns indicate extremely strong space-time curvature and tidal forces, and they become infinitely strong at the point itself.  An object near this singularity would be sheared apart in space and in time -- some of it thrown into the past as well as the future.




The two other points are the ones in the center of the loops, and represent locations around which time is flowing in circles.  They are singularities, but once again they are not gravitational singularities.  Instead, they are "rotational" singularities.  You could escape from near one, but you would be forced to spiral around and around in both space and time, before finally getting spat out into the future.   (Also, since this diagram only shows one dimension of space, these two points are actually a spherical surface in 3D.)

What could possibly cause space-time to behave this way?  I haven't the foggiest idea.  This kind of metric is totally unphysical -- it can't exist in our universe.  

Anyway, now perhaps you can see ways of playing around with the space-time metric to make weird things like this happen.  We could also get an object to exist inside of itself without involving CTCs, but it still requires having regions where time is locally flowing backwards.  For instance, we could have something like this:



Here there is a region where time flows backwards for a little while, at the same time that the space is collapsing, and then it reverses again and smooths out.  In this case it does this without making any closed loops or singularities, and what we get is an object that is nested inside of itself three times, the middle one moving backwards in time.

But again, I have no idea what sort of real space-time could do this, and it's probably still completely unphysical.  


In summary, what would happen if you distorted space-time enough to make an object be inside itself?  For starters, there would need to be a region where time is locally flowing backwards.  Beyond that, what happens depends on the type of distortion we made, and the potential for weirdness is very high.

I think I have found a way to create artificial gravity without a centrifuge. I just need someone to tell me if it would work or not. This method involves using an alcubierre drive to expand space above the ship and contract space below the ship so that the space inside the warp field is accelerating at 9.81 m/s^2. Meanwhile, the ships thrusters counter it with an upward force that would accelerate the ship upward at 9.81 m/s^2 (relative to itself) so that the force from the alcubierre drive and the thrusters cancel each other out and the people inside would experience gravity at 9.81 m/s^2. SO can someone tell me if this would work? I am not educated enough on alcubierre drives, so the only problem I can see is that an alcubierre drive only creates velocity, not acceleration. But again, I don't know.

Hornblower, first problem is you need an Alcubierre drive and the second problem is the field layout is determined by the direction of motion.  It could probably be shown to work in some way or another by making up some layout of spacetime, Watsisname is your guy for that, but it doesn't seem very practical.

If tractor beams are possible those maybe could be used to fake gravity with light.

if the Moon were suddenly given an earth-like atmosphere, how long would it take for the solar wind to shear it away?

John Boone,

Not long.  Even without the solar wind, the atmosphere would simply evaporate away.  Atoms in a gas have a distribution of speeds, and for lunar gravity a significant portion of those atoms would be moving fast enough to escape, so the atmosphere would boil away very quickly (hard to say exactly how fast, but probably a timescale of a century or less).

Hornblower,

Your logic is good.  Use the Alcubierre warp drive to produce acceleration.  Since this acceleration is not felt by those on board (the ship is on a freefall path), use thrust to cancel that acceleration, and this is felt as artificial gravity on board.  Or in other words, we're making artificial gravity with conventional thrust, then cancelling the thrust with warp.  Clever, and I was almost convinced it would work (insofar that warp drives are possible, and they most likely aren't.)  

Unfortunately there is a subtlety to how the warp drive works which, I think, breaks this scenario.  Here's why:

The description of the Alcubierre drive comes from solving Einstein's equations backwards.  Instead of taking a distribution of matter and energy and solving for the space-time geometry it produces, we start with the metric of space-time that we want.  In this case we want to find a metric in which there is a free-fall path with an arbitrarily fast speed, perhaps even faster than light relative to the rest of the space-time.  Then, if you place a gravitational test particle (approximating the ship) on that path, it simply goes along for the ride.

Problem: if we apply thrust to the ship, then we're no longer on the free-fall trajectory defined by the warp bubble.  The very foundation of the Alcubierre solution breaks down.  Follow a different path through the space-time, and you change the properties of the warp bubble you must be in.  To be at rest with respect to the rest of the space, there must be no warp bubble at all (the warp bubble must move).  So... I actually think this situation is unphysical even in the context of a warp drive.  You can't be both in a warp bubble and at rest relative to the exterior space.

Sorry. =(  It was a good idea.

One other side-note I'd like to make:

This method involves using an alcubierre drive to expand space above the ship and contract space below the ship so that the space inside the warp field is accelerating at 9.81 m/s^2.

The Alcubierre drive doesn't actually work by expanding and contracting the space (although that is what it does, and the idea that this is what enables it to go FTL is common and conceptually appealing.)  But the expansion and contraction of space are just consequences of the particular metric that Alcubierre chose for his FTL solution.  It is actually possible to find a metric containing faster-than-light freefall trajectories that do not have this expansion and contraction.

So an Alcubierre drive could be seen more as a theoretical artifice in order to gain some perspective in time-space matters, kind of like an equivalent of a Turing Machine in computer science?

That's how I like to look at it, yeah.  It's useful in studying the mechanics of space-time, and it can be intellectually interesting in the way that some solutions of mathematical equations can be interesting, even if they don't have direct manifestations in reality.  

Of course, that's what we said about black holes before we realized that they are real things, but in this case there are more fundamental reasons for thinking that the Alcubierre solution is nonphysical.  Kind of like with white holes.