The shaved ice would cool down the soup faster, because it would melt faster. But after both were completely melted, it would have cooled down the same.

So I'm honestly curious - is 1-2 T the theoretical max for how strong a neodymium magnet can be? Or is there an easy, back of the envelope, way of calculating it? I tried to scale up a small one to the mass of the Earth, but couldn't find any easy way of doing it, but my estimate made it quite large.

Oh yeah, a magnet like that would kill you in so many ways, so fast. Of course it would rip the iron out of your blood, but that's child's play in the ways you'd died. Your neurons would become polarized and unable to fire. The cells in your body would all magnetize, ceasing any and all functions. You're toast.

This discussion here answers this.

It helps to think of how you'd actually send information via crossing two long sticks. Any method you actually come up with, will end up taking longer than just shining a light at someone.

Mostly.

That strong of a magnet would actually probably magnetize the rubber ball. Every material magnetizes under a strong enough magnetic field, but without knowing the specifics, it would be hard to calculate the effects.

The Sun will not supernova, but it will red giant. The reason being as the sun "uses up" it's hydrogen (in reality, it will only fuse about 10% of the hydrogen before transitioning), it will transition to new fusion chains which don't last nearly as long, but create energy significantly faster.

> can the crossing point exceed the speed of light?

Sure.

> does this mean you can essentially send information faster then the speed of light?

No. While there's no limit to how fast that "point" can move (since that "point" isn't a physical thing, just a concept), there's still a lag between you moving your levers, and the point of crossing moving.

A similar example, that is perhaps easier to understand- if you shine a really bright laser pointer at the moon, and then flick your wrist, you can make the "dot" of the laser pointer move across the surface of the moon as quickly as you want. That dot could move way faster than 'c'. But it doesn't break anything- because there's still the lag you'd expect from the time you pushed the button on the laser pointer, until the dot hit the moon to begin with.

While it's true energy is always conserved, kinetic energy is only conserved in perfectly elastic collisions. So, you are on the correct path at the end- inelastic collisions kinetic energy is converted into other types of energy, like heat, sound, deforming the bodies, etc.

If kinetic energy was conserved in the collision, then you would have the situation where the two objects bounced off of each other, and went in the opposite direction, at the same speed they came in.

Magnetic fields in planets/moons is caused by having a rotating, magnetic core, which Ganymede does. The size does not matter.

Wireless charging is a type of inductive charging, which works via an application of Faraday's Law. Essentially, if a magnetic field changes inside of a wire loop, it will induce a current in that loop. So, wireless chargers producing a time varying magnetic field, and the phone has a wire loop, so a current is induced, which is used to charge the battery.

Why isn't is used much outside of small, personal electronics? 1.) it's not super efficient. Only the energy that goes into producing the magnetic field that goes through the loops actually goes into creating power, the rest is wasted. 2.) It produces quite a bit of heat for how much power it makes. Make enough power to power something big, and it's going to get real hot.

I specifically talked about how there are models where the photon becomes a quasiparticle in my original answer to the question, I was simply explaining to the person who asked why there are complications when viewing EM waves moving slower.

This is, in a way, a simple question, but I think it can have some fun deviations.

So, if you haven't seen it before- here's a famous example of an astronaut dropping a hammer and a feather on the moon, and they hit the ground at the same time. This is an illustration of basic physics. You apply Newton's Second Law, which says F = ma, and you say the force of gravity is equal to mg, so you end up with

F = mg = ma

And so you can cancel m on both sides and just get a = g so you see the acceleration an object undergoes is not dependent on mass, so any object falls the same speed. And on the Moon, that works. And it illustrates the principle perfectly. Of course, there is a reason we did that experiment on the moon and it's so cool- it goes against what we feel should happen. On Earth, you drop a hammer and a feather, and of course they fall at very different speeds. The difference comes from the air resistance on the Earth.

Unlike gravity, air resistance is not a constant. It depends on a couple of things- like the shape of the object, the size of the object (and when we say size, we have to be specific. It's the size of the object in the direction of travel- the part of the object getting hit by the air) and the speed of the object (the faster an object is going, the stronger the air resistance is. The equation for air resistance is captured in the famous drag equation and says Fd = 1/2*p*(v^2)Cd*A where p is air density, v is the velocity through the air, Cd is the drag coefficient, which is dependent on the shape of the object (but not the size) and then A is the "reference area" (which is the surface area of the object in the direction of travel).

So, when in the presence of air, using Newton's second law things look a little different. Now you say:

F = ma = mg - 1/2*p*(v^2)Cd*A

(There is a minus sign between them because gravity and air resistance work in opposite directions, gravity pulls down while air resistance pushes up). Now, you can no longer cancel m because mass isn't in the air resistance equation. So, you can solve for a and say

a = g - 1/2*p*(v^2)Cd*A/m

So, when you look at the above equation, if the object has the same Cd and same A, and the mass gets bigger, then acceleration will be bigger (since the term you're subtracting off gets smaller), so in that case, you would say "the heavier something is, the faster it falls." And the works to a certain point. Say, a child's toy ball filled with air vs a bowling ball. About the same size, same Cd (since Cd is just based on shape) and so about the same area, so the more massive bowling ball falls faster. Or a more dramatic example. A piece of paper, or a piece of plywood cut to the same size. The two objects have the same Cd and A, but the plywood is more massive, so it falls faster.

But of course, a lot of times, when something gets more massive, it also gets bigger, so then A would increase as well. So, really, what matters for two objects the same shape, is the ratio between the surface area and the mass. Now, since volume of a sphere (and thus mass) grows with the radius of the sphere cubed, and surface area only grows with radius squared, a large bowling ball that's made out of the same material as a small one will still fall faster (since the mass to surface area ratio is still higher), but a small, dense bowling ball that still weighs less than a larger, less dense bowling ball, could fall faster.

Now, taking this a step further, we have always been operating under the equation that the force of gravity is just mg which is a really good approximation when the thing that's being dropped is much smaller than the thing it's being dropped on, but if we use Newton's law of gravitation we'll see the equation should really be

Fg = -G*m1*m2/r^2

where G is the gravity constant, m1 and m2 are the two masses, and r is the distance between them. So, this shows, perhaps unintuitively, that when you drop a bowling ball on Earth, the bowling ball is pulling just as hard on the Earth as the Earth is on the bowling ball. However, since F = ma since the forces are the same, but the mass of the Earth is so much bigger than the mass of the bowling ball, the acceleration of the Earth is much much smaller than that of the bowling ball, so the acceleration of the Earth is essentially zero. However, what if instead of dropping a bowling ball on Earth, we dropped Mars? Now, while Mars is still a lot smaller than Earth, isn't not so much smaller that the acceleration of Earth would be essentially zero. So, in this case, if we dropped the Moon on Earth vs dropping Mars on Earth, Earth and Mars would collide quicker than the Moon and Earth (assuming dropped from the same height) because Earth would accelerate more towards Mars than it would towards the Moon, because Mars is a lot more massive than the Moon.

The problem is that according to General Relativity, a massless particle must always travel at c. So when dealing with the photon nature of light, a photon cannot slow down. But of course, we know light propagates slower through a medium, so somehow you have to reconcile these things.

Sorry, I should have been more clear. You can, right up until the point where they collide (you can think of as getting close enough their wave functions overlap), at which point you can no longer know which particle is which.

While it's true if a single photon is absorbed by a single atom, you cannot predict which direction the photon will be re-emitted, so how is this different? Well, the process is not so different from light "reflecting" off a mirror- while we say light reflects, a mirror is also an absorption and re-emission situation, and obviously those don't go in a random direction.

The answer comes down to conservation of momentum and interference. Since the incoming photon has momentum, there is a higher probability that the photon will be emitted in the same direction to conserve momentum. Obviously, not all of the photons are emitted in that direction, but due to the probability there will be constructive interference in the same direction and destructive in all other directions. In general, things like Snell's Law of Refraction, and angle of incidence equalling angle of reflection occur with large numbers of photons, and they do not describe what happens when a single photon is absorbed.

So, first answering your main question- elementary particles are all fungible. That means, they are truly identical, and they are impossible to label. So, if a photon is absorbed and then remitted, it doesn't really make sense to say "is it the same photon or a different one?" There aren't really "same" or "different" photons, there's just photons, unlabeled.

And it's not just photons. Any time you have a particle collision which results in some different elementary particles (like the ones from particle accelerators), if one of the products and reactants are the same elementary particle, you can't answer "is this the same or a different particle?" It's a particle. That's all you can say.

Now, to get into the can of worms you opened, and probably didn't even know it. It is this line:

> It is my understanding that the light is slowed through the medium because photons are absorbed and then re-emitted repeatedly.

I always say, if you want to get some physicists to fight, ask them why light propagates slower through a non-vacuum. You'll get a different answer from each one, and they will pretty aggressively defend their position and discount the others. I always find it fascinating, because it seems like a pretty simple question (why does light travel slower in a non-vacuum?) but the answer is quite complex, and our models for it all work, but tell slightly different stories.

The easiest to understand model is the one you mentioned- and it does work. The most common complaint is that an atom can only absorb very specific wavelengths, but light of all wavelengths is slowed down by materials. But, this is handled by understanding that collections of particles will have nearly an infinite number of modes of excitation- you can cause groups of particles to vibrate or rotate, you can cause vibrations between groups of 2 particles, or groups of 3 (or 4, or 5....). There's a ton of different excitation modes, and for a dense medium, you can absorb and re-emit any wavelength of light.

Other people will express a model where light actually takes many paths through the medium, and that superposition actually results in it appearing as if the light is traveling under 'c'. Still others will talk about how photons become a quasiparticle when in a dense medium, and that particle doesn't travel at 'c'. And I'm sure there are others out there. All of these explanations "work" and I won't say one is right over the other.

> if you choose the right reference frame, it would seem that the return trip requires the twin to experience negative acceleration.

While in relativity velocity is relative, accelerations are not. Accelerations can be measured and felt. Easiest example. You're driving along a perfectly flat road in the back of a windowless truck. There is no experiment you could do to determine what speed you're going. All speed feel the same. But if the truck accelerated- sped up, slowed down or even turned, you would notice.

Before calculus you probably took a class where you did lines (slope/intercept form, etc), right? Think about all the word problems where you wanted to know the slope of the line- when you wanted to know "rate of change" or "how much more it costs to build one more object" or anything like that. All of those types of problems require calculus if you want to do them for anything more complicated than a line.

As an example- perhaps you had a problem like this:

> A car is traveling down a race track in a straight line. At t=10 seconds it's 100 meters down the track, and at t = 20 seconds it's 150 meters down the track, how fast is it traveling? Where did it start on the track?"

So, you find the slope and intercept of the equation, and say "oh, it's traveling at 5 m/s, and it started 50 m down the track.

But if the car isn't traveling at a constant velocity, instead you say "at t = 0 seconds a car starts from rest and is 100 m down the track. At t = 10 seconds, he's 200 meters down the track, and he was accelerating the entire time. How fast is it traveling 2 seconds after it starts to accelerate?" well now you need to use calculus. You need to find the slope of the tangent line to the equation that describes his position. You hear physics terms a lot because in general, velocity is the derivative of position, and acceleration is the derivative of velocity (aka- the tangent line to the position graph is the velocity, and the tangent line to the velocity graph is the acceleration, just like the slope of a line in a linear graph is the velocity).

Classical physics cannot describe quantum physics- but quantum physics can replicate classical. The main reason we don't use quantum physics in the classical realm is because it's far too mathematically challenging for large systems.

This Q&A might be helpful for a better understanding.

It's not quite right to say that "time stops at the speed of light." It's better to say "time becomes undefined at the speed of light." But what's interesting is, so does length due to length contraction. So using layman's terms, you could say time stops, but also, it doesn't have to go anywhere, because lengths are all zero.

Dark matter was originally theorized to explain discrepancies between scientific predictions and measurements. But it turns out, it has predictive power. When we estimate the amount of dark matter we think there must be in the universe, it actually explains the relative amounts of Hydrogen and Helium we see in the universe now.

Apparently it was junk they ejected. It will enter the atmosphere soon to burn up.

Almost all of the non-star things we can see from Earth are gravitationally bound to our Sun. The other planets, the asteroids and comets, moons, etc are all part of our solar system, which means they are bound to the Sun. Most of the planets have nearly circular orbits, so they have very repeatable, normal patterns, while some of the comets and asteroids have highly elliptical orbits (spend a little bit of time close to the Sun moving fast, but spend most of their time far away from the Sun, moving slow). It's these comets with highly elliptical orbits that have these odd patterns you're mentioning. Probably the most famous comet, Halley's Comet has a very high eccentricity (of 0.96. 1 is the max eccentricity, Earth's is 0.016), meaning it can be up to 35 AU (1 AU is the average distance from the Sun to the Earth), and down to 0.5 AU.

What does it mean to be gravitionally bound? One way of thinking about it is that the total energy of the system (system being object orbiting and the object it's orbiting) is negative. How is it negative? Traditionally we consider gravitational potential energy to be negative- and it gets more negative the closer you get to it. Kinetic energy is positive, increasing with speed. So, if the sum of the kinetic energy + potential energy is negative, then the object is "gravitionally bound" to the object it's orbiting. This is how you calculate escape velocity, and another way of saying it is that the comets are traveling at less than the escape velocity of the Sun.

The voyager spacecraft are well above the Solar escape velocity so they will be traveling on out of here.