ELI5: Answer an ELI5 FAQ- Zeno's Paradox, The Grandfather Paradox, Einstein's Twin Paradox and Schrodinger's Cat

I remember a time about 3 years ago when the Schrodinger's question was weekly, so I had a book marked reply ready.

The twin paradox:

The idea of the twin paradox is relatively simple. You have two identical twins, and one of them stays on Earth while the other flies away on a spaceship at a relativistic speed for a while and then returns to Earth. When the traveling twin gets back, he realizes that his Earth-bound twin sibling is much older than him.

Relativity predicts time dilation. That is to say that that if you are moving at a very high, constant velocity relative to me, I will see your clocks ticking slower. So that explains why the Earth-bound twin would age more than the traveling twin.

However, relativity also says that motion at constant velocity is relative. If you are moving at a very high, constant velocity relative to me, I am also moving very high, constant velocity relative to you, and by the same logic as above, you should see my clocks ticking slower. And that's true. In this case, we both see each others' clocks ticking slower. (Remember, we're both moving at constant velocity; there are no accelerations here.)

So why is it that both twins don't end up at the same age? Why does one age "normally" and the other age "slowly"? How does nature "know" which twin should be older at the end of the experiment?

The answer lies in the fact that the traveling twin has to turn around in order to come back. By turning around, they have changed their inertial frame of reference (in simple terms, they must have accelerated at some point in order to turn around and return to Earth).

Here is a diagram of the situation. This is called a Minkowski diagram, and it plots how things "move" through spacetime. The horizontal axis represents distance in the direction of motion, and the vertical axis represents time (multiplied by the speed of light so that it has the same units as distance). The line labelled "outgoing worldline" represents the trajectory of the twin in the spaceship, and the vertical line "worldline of A" represents the motion of the Earth-bound twin. The worldine of the twin on Earth is a vertical line at x = 0, meaning that they stay on Earth for all time. You can see that the twin in the ship moves away from x = 0 (Earth) at some constant speed. So far, both twins have only moved away from each other at constant velocity, so they both see each others' clocks ticking slower, by the same logic as above. But then the twin in the ship turns around (this is represented by the "kink" in the worldline, or the corner in the triangle that sticks out on the right). Now the twin in the ship has changed inertial reference frames, and begins to head back to Earth at the same constant speed as before, but in the opposite direction.

Now the symmetry between twins is broken. The twin in the spaceship changed reference frames, and the twin on Earth didn't. So by the time the traveling twin gets back to Earth, the Earth-bound twin will have aged significantly more than they have. This is indicated by the red "lines of simultaneity."

Zeno's Paradox:

There are actually multiple Zeno's paradoxes, but the one that seems to be most common is some variation on the following. You want to travel to a point one mile from your starting point. To do that, you first half to travel halfway there - 1/2 mile, leaving 1/2 mile remaining. Then you have to travel halfway across the remaining 1/2 mile - 1/4 mile, leaving 1/4 mile remaining. Then you have to travel halfway across the remaining 1/4 mile - 1/8 mile, leaving 1/8 mile remaining. You can keep repeating that forever, since you can always divide up the remaining distance by half. So how do you ever reach your end point?

There's the cop-out answer that eventually the distances will get so small that you can't travel less than that distance, but assume that we're playing in abstract math-world, where dividing up a distance infinitely many times is possible. And that is what's going on here: 1/2 + 1/4 + 1/8 + 1/16 and so on will eventually equal 1, but only with an infinite number of pieces. Additionally, that's an important piece of the puzzle: you can add an infinite number of terms and get a finite answer.

The question then becomes how fast you're traveling. If you travel each piece and take a one-second break between each one, you won't ever reach your end point (i.e., if you take each distance as an actual step instead of covering a bunch of the really small ones with a single step). Something that takes one second over infinitely many repetitions means that you need an infinite amount of time.

But let's say you decide to travel 1 mile per hour for the entire process, without taking any breaks when you reach a new halfway point. The first 1/2 mile would take 1/2 an hour, the next 1/4 mile would take 1/4 hour, the next 1/8 mile would take 1/8 hour, and so on. It turns out to be the same formula as for the distance: 1/2 hour + 1/4 hour + 1/8 hour + (and so on) equals 1 total hour, just like you'd expect (1 mile per hour over 1 mile = 1 hour). Again, you can add up an infinite number of pieces and get a finite answer, but this time, you're adding up times instead of distances.

So, just like you'd intuitively expect, you will reach your endpoint.

Before covering the grandfather paradox, it is important to note that a paradox is a statement, not an event.

The grandfather paradox supposes that you have a time machine, and that for some reason, you plan to use it to go back in time to kill your grandfather. However, if you kill your grandfather, it would inadvertently kill you as well, and then you could never go back to kill your grandfather, which means your grandfather would still be alive. The paradox is meant to show the complexity of traveling backwards in time. It is, at its simplest, an unanswered question: if you travel back in time, what happens when you do something that prevents you from going back in time?

an old Schrodinger's cat one from me

According to one interpretation of quantum mechanics, certain particles are both decayed and not decayed all the time, and only have to "choose" one state after they are measured.

Schrodinger thought that was ridiculous. To illustrate why, he made an analogy. Imagine you had such a particle, hooked up to an apparatus that would kill a cat in a box if the particle decayed. Schrodinger's point was that, at the macro scale the theory was ridiculous: even if we could pretend that a particle was both decayed and not decayed, surely it was ridiculous for the cat to be both alive AND dead until you opened the box.

People ended up liking the analogy more than the argument, and so Schrodinger's cat just became a way to talk about the weirdness of quantum physics. Because of the example, it also often confuses some people, leading them to think that the cat/particle is alive OR dead (decayed OR not decayed) until someone looks, rather than alive AND dead (decayed AND not decayed).

Also, a good explanation from another person here: https://www.reddit.com/r/explainlikeimfive/comments/39393l/eli5_can_someone_break_down_schrodingers_cat/crzzzl9

The Grandfather Paradox is one of the issues related to time travel. Since backwards time travel isn't possible, it's like those proofs that 1=2 which use division by zero. You can't predict scientifically what will happen in a scientifically impossible situation. To say "If backwards time travel was possible?", then you need to explain your theory for it.

It does make some wonderful speculative fiction.