The 18 quadrillion is to get out to 1600 light years, as opposed to 100 light years as /u/mfb- is talking about.

Sorry, I shouldn't have implied there was no interesting science to be done with entangled particles and black holes, I meant to just say there is no way of using entangled particles to get information out of the event horizon of a black hole

Yeah. I combined "Alpha Centauri" and "Proxima Centauri" in my mind somehow.

But over long distances, it re-becomes inverse square again. After the waist of a laser beam, it spreads out like an inverse square law again, and when you're dealing with lightyears, most of the spread will be after the waist.

The Sun's gravity is always tugging on it.

Nothing would happen.

You can read up on what Quantum Entanglement actually means in this thread.

Sadly, PopSci has completely misrepresented Quantum Entanglement, and it doesn't mean what most articles about the topic says it means.

The nearest black hole to us isn't 1.6 lightyears away, it's 1600 lightyears away.

First, some terms. There is "true north" and "magnetic north." True north is perpendicular to east. Magnetic north is close to perpendicular to east, but not quite.

True north is defined as the point that Earth's rotation axis points through. To visualize, look at this globe. The "true north" pole is where the pole sticks through the globe, the place the Earth is rotating about. This is what is perpendicular to east. Which, when you think about it as a rotation, makes sense. As the Earth rotates, the Sun is going to appear to rise in the direction the Earth is spinning. This globe photo may help illustrate that if it's not clear as of why.

Now, magnetic north is based on the magnetic field of the Earth, and it is close to truth north, but the true north pole is about 1200 miles away from the magnetic north pole. In the latitude bands most people live in, that distance doesn't matter much- if you point true north of magnetic north, you're basically pointing in the same direction- but as you move really far north (or really far south), that distance matters more.

So, is it a coincidence that magnetic north and true north are close to aligned? No, it's also due to rotation. The Earth's magnetic field is caused by spinning liquid metal in the outer core, and that core's direction of spin is highly influenced by the direction of the Earth's rotation. So, most of the the time, the Earth's magnetic field is close to aligned with the Earth's rotation axis. Since the Earth's magnetic North pole was discovered, it has moved by 600 miles. The Earth's magnetic field will also flip-flop at some point in the future (Magnetic north pole will go to the geographic south pole) and has flip-flopped in the past. During this flip-flopping time, the magnetic north pole will have to wander all the way down the globe, and thus magnetic north and true north will be no where close to each other (and at some point, magnetic north will lie due east!). But most of the time, the Earth's magnetic field stays relatively aligned to the Earth's rotation.

(This is sort of going down a rabbit hole, but you can watch this video about why Canada labels their runways using true north, while most of the rest of the world uses magnetic north, but it comes down to how those little variations in where magnetic north is don't impact much, unless you're really far north or south)

> it may take decades to get to one

This is the main problem. It wouldn't take decades to get to one, it would take hundreds of thousands of years.

Voyager is the furthest probe ever launched from Earth. It has been traveling for over 45 years and has made it 0.06% of the way to Alpha Proxima, the closest star to Earth- and it's still slowing down. The closest known blackhole to Earth is 400 times further away from Earth than Alpha Proxima..

Of course, even if we got a probe there, it would have to have more power than any transmitter ever made to communicate with us. Transmission power falls off using an inverse square law meaning you would need ~18 quadrillion times more power to communicate back to Earth from that blackhole than it would take to communicate back from Mars.

And to top it all off, even if we somehow conquered all of that- once the probe actually entered the blackhole (aka- crossed the event horizon) it is physically impossible for it to send us information anyway, since nothing can escape a blackhole's even horizon.

To the best of our understand, particles are fundamentally wavelike in nature. For example, if you shoot electrons through closely spaces slits, they will form interference patterns just like light does (There are lots of other experiments you can do to demonstrate this as well, but this is perhaps the most straightforward one). So, if the wavelike nature of particles is fundamental (which we believe to be true), then the Uncertainty Principle is also fundamentally true. In fact, the Uncertainty Principle can be derived, without any reference to “measurement” at all.

There are actually many different uncertainty relations- the Heisenberg Uncertainty Principle being the most famous one- that there is an uncertainty between the position and momentum of a particle. But really, any two observables (observable being a quantum mechanics word for “something you can measure”) which do not commute will have an uncertainty relation. What does this mean? So, when something commutes, it means order of operations doesn’t matter. For instance, A + B = B + A. Addition commutes. Multiplication sometimes commutes. For instance, if x and y are just numbers, then xy = yx. But, if x and y are matrices, then x*y ~= y*x. In Quantum Mechanics, operators (or functions which operate on the wavefunction) sometimes commute and sometimes don’t. Ones that don’t (like position and momentum), will always have an associated uncertainty principle.

Position and Momentum are part of the canonical commutation relation. This means if the position operator (P) operates on the wavefunction (W) first, and then the momentum operator (M), you get a different answer than if the momentum operator operates first, and then the position. Or in math: [XP – PX]*W = i*h_bar, where i is the imaginary number, and h_bar is Plank’s constant divided by 2*pi. Another common pairing that shares this relationship is Energy and Time, thus they also have an uncertainty principle.

While perhaps this got pretty far into the weeds, the Wikipedia article summarizes it nicely:

> Historically, the uncertainty principle has been confused with a related effect in physics, called the observer effect, which notes that measurements of certain systems cannot be made without affecting the system, that is, without changing something in a system. Heisenberg utilized such an observer effect at the quantum level (see below) as a physical "explanation" of quantum uncertainty. It has since become clearer, however, that the uncertainty principle is inherent in the properties of all wave-like systems, and that it arises in quantum mechanics simply due to the matter wave nature of all quantum objects. Thus, the uncertainty principle actually states a fundamental property of quantum systems and is not a statement about the observational success of current technology. Indeed the uncertainty principle has its roots in how we apply calculus to write the basic equations of mechanics. It must be emphasized that measurement does not mean only a process in which a physicist-observer takes part, but rather any interaction between classical and quantum objects regardless of any observer.

That's true. You will continue to accelerate until hitting the surface. And the speed you'll be accelerated to is the escape velocity. And it's because your starting and end states are the same, just in reverse.

When calculating escape velocity you're saying "how fast do I need to launch myself from the surface of the planet, so that I don't come to rest until infinity?" But for this question you're saying "if I'm at rest at infinity, what speed will I have when I hit the surface of the planet?" Since the start and end points are the same, the speeds are also the same.

The maximum speed the planet could accelerate you to, assuming you're starting at rest, is the escape velocity of that planet.

To truly reach that velocity, you'd have to start at a distance of "infinity" away from the planet. Obviously, you can't start at infinity, but even starting out relatively close- like the distance to the Moon, gets you within 99% of Earth's escape velocity.

What is kind of cool is, the way you calculate escape velocity is basically the exact same calculation to calculate the maximum speed a body could get you to. It all comes down to conservation of energy. The argument goes: Energy is conserved. If you start at an infinite distance away from the Earth, at rest, your total potential energy is zero, and your kinetic energy is zero. So, as you fall towards Earth, your total energy must stay zero. Since kinetic energy is positive, and potential energy is negative- the closer you get to Earth, the more negative your potential energy must be, and thus your kinetic energy has to grow to keep it at zero. So, at any distance, r, from the Earth, if you started at infinity and moved towards the surface, you could calculate your speed as follows:

1/2mv^2 - GMm/r = 0

cancel m and move over the potential energy term

1/2v^2 = GM/r

Solve for v

v = sqrt(2*G*M/r)

It doesn't take energy to apply a force. Think of a book sitting on a table. Gravity is pulling the book down (aka, a force pulling down) and the table is pushing up on the book (aka, a force pushing up). And it can just sit there forever. Obviously the table doesn't need energy to do that.

No different than the Sun keeping the Earth in orbit. The energy of the Earth/Sun system stays constant (assuming nothing else in the universe). The force the Sun is providing on the Earth isn't changing its kinetic energy (since kinetic energy only depends on the speed of the object, not its velocity), so conservation of energy doesn't get violated here.

Everything you're saying holds up, except for this one thing:

> a beam that cannot flex and is incredibly long

In physics, we often times talk about "rigid bodies" and make the assumptions that they are infinitely stiff, but that's just a "small thing, moving slow" assumption- where they appear to be completely rigid. In real life, materials are not completely rigid.

Now, you might think "that's just an engineering problem, we can just design something to be really stiff. But you can't. Information- including compressions and rotations, travel through a material at that material's speed of sound. Which makes sense if you think about it, sound waves are compressions passing through a material.

So, if you had a really long rod, and you started rotating it faster and faster, the rod would start to bend and then shear. And that's not an engineering problem- it's a real physics one.

> Is each star within a galaxy assumed to be a point mass?

Here's what's cool, using Guass' Law for gravity you can derive the Shell theorem which says that for spherical objects, if you are outside of the mass of the object, then the gravity of the object is the same as if all of the mass is concentrated at a point right at the center. So, yes we get to treat them as a point mass, but that's (barely!) an approximation (I say barely because stars are not perfect circles, they are slightly bulged due to rotation. But this is such a minor effect, it wouldn't really cause an issue).

> Do we "simply" count the stars, and their mass, and get that as the mass of the galaxy, and then based on its size, work out if it should be capable of staying together? Or do we model the individual stars and their gravity?

To answer this, let's talk about something like a space shuttle orbiting the Earth. In Low Earth Orbit (LEO) a space shuttle travels about 17,500 mph (24,000 kph) to stay in orbit around the Earth. If it went too slow, it would fall into the Earth. If it went too fast, it would fly away from Earth and never return. The speeds are a function of the mass of the Earth. That is- if the Earth was heavier, the space shuttle would have to go faster to stay in LEO, and if it were lighter, it would have to go slower. Another cool thing is, the size of the object orbiting doesn't really impact it much at all (this is true as long as the object orbiting is much much smaller than the object being orbited). So, if we looked at some alien planet with a high powered telescope that had a satellite, and saw how fast the satellite was orbiting the planet, we could know the mass of that planet.

The stars in a galaxy are similar, but instead of orbiting a planet, they are orbiting around the galaxy. But all of the stars closer to the center of the galaxy are like the planet the stars are orbiting around. And if we take the link above on Shell's theorem even further, what's cool is if we model the galaxy as a rotating, flat disk (which it's not, and in the real simulations they do it more accurately, but honestly, modeling the galaxy as a disk is "good enough" for this), then it turns out that at any point on the disk, the gravity is completely determined by the amount of mass "closer to the center" of the disk then the point- that is, all the mass further away rotating doesn't matter. Why? Well, you can think of it like this: you're getting tugged both ways by mass further away from the center than you. The mass "behind you" is closer, and pulling you away, but there's more mass "in front of you", pulling you in. If you do all of the really complex math and add up all of those forces, it turns out they completely cancel. It's really cool.

So when we look at how much mass we can see between a star and the center of the galaxy, the star is orbiting at a speed that requires there be more mass than there actually is. Going to the shuttle example above, it's like if a shuttle was orbiting a planet that looked like Earth, but was moving at a speed like it was orbiting Jupiter, we'd say "wow, there is something weird in that planet, it has way more mass than it looks like." So, likewise, when we look at the galaxy we say "wow, there must be more mass in the galaxy than we can see, because the stars at every radius are just moving faster than we think they should be." That was the initial inspiration for Dark Matter- matter we can't see, but still creates gravity, giving more mass to the galaxy than we'd could otherwise see.

> If we do model the individual stars, do we model their cumulative gravity to infinity too?

Yeah, we can easily model their gravity out to infinity. The equations are simple for a computer to crunch through out to any distance.

A truly uniform gravitational field is inertial, yes. But those don't really exist (we say, for instance, that on Earth the acceleration due to gravity is -9.8 m/s^(2) but there is a slight height dependence on it). So, things in free fall (without air resistance- including orbits) we will say they are in "locally inertial" frames. But even in the ISS, there will be slight tidal forces acting on you- aka, the side closer to Earth will have ever so slightly more gravity than the side further away.

Correct. The resolution of the twin paradox involves knowing which one accelerated.

So, it is true. Trying to calculate the time dilation between Earth, and say, some planet on the opposite side of our Milky Way would be very, very difficult. But at the same time, compared the the speed of light, we know those other planets are moving really, really slowly, and thus the differences are minute.

Rotation is an acceleration. Your velocity is always changing.

Relativity doesn't say "all frames of motion are equally valid." It says "all inertial frames of motion are equally valid." That word "inertial" is doing a lot of work- it means the reference frame cannot be an accelerating frame. When you're spinning, you are in an accelerated frame, so we do not consider that "just as valid" as any other frame.

Now, that might seem like an arbitrary distinction- but it's really not. The reason is- acceleration can be measured, speed cannot. That is, if you are accelerating, you can perform an experiment/take a measurement that would determine if you were undergoing that acceleration. That is, if you were in a car, accelerating towards a wall, you don't have to say "I wonder if I'm accelerating towards the wall or the wall is accelerating towards me." If you're accelerating, you can feel it- you get pressed back into your seat, etc. But if you are moving at a constant speed towards a wall, there is not experiment/measurement you can do which answers "am I moving towards the wall, or is the wall moving towards me?" Sure, you might have to say "man, the wall, the ground, and everything around me is moving towards me" so in some logical way you could say "so obviously I'm the one moving" but there isn't anything that you can do to "prove" it. Another way of putting it, accelerations are absolute, speed is always measured in relation to something.

You're correct, it has to do with acceleration. This question has a name, the Twin Paradox and solving this requires a more complex application of relativity than is normally taught until grad school- but essentially, it all comes down the the acceleration.

I'm of the belief the best way to learn how to program is to choose a difficult, but "fun" (fun being fun for you, something you're interested in) project, and then just push through trying to figure out how to do it.

If you have literally no programming experience, you'll probably have to do some sort of classes (like an MIT Open Courseware class or something) just to learn the basics- but then just start on your difficult project, get stuck a bunch, ask questions (every programming language has a Reddit community), and push through.

I have found people get a lot more (and are much more willing to push through) working on something they actually care about, instead of pre-canned exercises.

The only orbits which pass over the same part of the Earth each time around are geosynchronous orbits (geostationary orbits are geosynchronous orbits which have a 0 degree inclination- aka, they are directly above the equator). All other orbits will "track across" the globe. The path they take across the globe is referred to as their ground track. There are special satellite orbits called "Earth-Repeat orbits which will, after every so many revolutions, repeat the same ground track. However, these are a special case and take special planning to achieve.

To understand why, you can think of how the satellite orbits- it doesn't care the Earth is rotating. Essentially, it's orbit would not change if the Earth was rotating once every 24 hours (like it does now), or once every 12 or 36. If you were observing the satellite from a "fixed point" relative to the Earth- aka, a point orbiting the Sun with the Earth, but not orbiting the Earth, you would see each satellite repeating it's orbit with the Earth rotating underneath. To see some good pictures of how all of this works, I like this write-up.