On the whole monkeys type Hamlet exactly as Shakespeare wrote it, isn’t it even more statistically improbable that Shakespeare would write it exactly as he did?
I suppose The Bard would have been limited by combinations of letters that make words, and word combinations that make lexical sense – but he also could have made it arbitrarily shorter or longer, by even one letter or word (or near infinite letters or words – Hell, he could’ve done Act XI)
So why is a Monkey writing Hamlet always used as the paragon of example of wildly improbable event, when something even more wildly improbable has happened vis-a-vis the very same text? If Hamlet happened, monkeys coming along afterward and writing it up is easy-peasy.
It’s more improbable that Shakespeare would write Hamlet exactly as he did than a monkey would type it exactly as he wrote it.
But, get this: It’s even more improbable that Shakespeare would have typed Hamlet exactly as he wrote it – even more improbable than a monkey typing it. KA-POW
This blew my mind. I was so used to the idea of the moon dragging water around the planet that I never even considered the notion that the tide happens daily and not monthly. It’s like I took the red pill and observed the infinite ignorance.
That was the simple explanation I had always heard as a kid, but my understanding now is that the centrifugal part of the explanation in @MikeR 's PDF is actually a necessary competent. It’s not enough to just say that the Earth is being pulled more than the water on the far side, there’s actually a force bulging it away on the far side, and, likewise, an actual force pulling it inwards on the sides.
For this same reason, I don’t think of the moon were just side-by-side as in @Bumperactive 's scenario it would necessarily form a double-bulge. The rotation is necessary.
Edit: Wow is this a rabbit hole of confident-sounding conflicting opinions. This is more complicated than I first thought. My understanding of this paper, though, is that centrifugal forces are still relevant, but the explanation in @MikeR 's PDF isn’t correct, because it has one of the arrows of the centrifugal force wrong. The paper is hard to understand, though, because it first calls that explanation the “correct” one, and then explains why it is incorrect:
… if we’re willing to learn enough about “centrifugal forces” to understand that they are both “real” and “fictional” at the same time, we can explain tides in terms of a rotating reference frame if we want
but it’s never necessary — these things can always be described in an inertial frame with no centrifugal forces
Remember centrifugal force isn’t its own thing, though, it’s an apparent force that comes from being in an accelerating reference frame. If you are spun around on a carousel, you feel centrifugal force pulling you outward, but from the perspective of someone on a ground that’s just your tendency to move in a straight line and the only real force is the one pulling you in.
It’s the same thing here. From the perspective of someone here there’s a centrifugal force away from the moon and that lifts the ocean on the far side. From the perspective of someone watching in space, the earth is being accelerated to the moon faster than the water, so it gets left behind. The two are entirely equivalent.
And yeah, if you were to have the earth and moon moving straight toward each other, there wouldn’t really be a centrifugal force but there would still be an inertial force doing the same thing. There has to be, since the difference in acceleration would still be there for the outside observer. The paper you found actually does say as much.
Edit to add:
That Matsuda paper does also point out a legitimate complication for talking about centrifugal forces – the ones in Fig. 3 are drawn as if the earth is orbiting around the moon, but in reality it’s orbiting around a center of gravity inside itself, so properly the centrifugal forces are as in Fig. 4. The rest of it is basically explaining why Fig. 3 gives the right tides anyway. That makes it a lot simpler to understand if you stick to the non-accelerating reference frame and just talk about the moon’s pull instead.
here’s my non sciency way of understanding what @chenille and @smulder are saying:
when something’s in orbit, it’s essentially falling. infinitely. ( it’s got enough forward momentum to miss colliding, but not enough to get away. ) the moon and the earth are always falling around each other, so the (wave of) water on the far side of earth is always going to be lagging behind in the fall - making it appear to be bulged.
You might be interested to know that the “solid” ground (crust) is also still slowly rebounding from the ice age where is was covered under the weight of 4000 ft or more of ice, such as around the Great Lakes.
If you just popped the Earth and the moon down in space next to each other, then they’d move towards each other until the crashed, but yes, the water nearest the moon would ‘rise’ up as they got closer. I’m pretty sure you’d also get a bulge of water on the far side of the Earth though, as that water was ‘left behind’ the Earth (ie, inertia).
Now, if you had the Earth and moon orbiting, but they were both tidally locked (ie the Earth rotating at the exact speed the Moon is orbiting, so it appears fixed in the sky*), you’d have a bulge of water nearest the moon, but I think (not sure), that you wouldn’t have a bulge on the far side. I’ve got a degree in Physics, but I’d still not put money on it.
*the Moon is already tidally locked, which is why we only ever see the same face of it, and eventually the Earth would get tidally locked to the moon, if the sun doesn’t destroy both by then.
since the force of gravity varies with distance, there are differences in potential between the near side, the middle, and the far side
if the objects were locked to each other, there would not be a noticeable lunar tide because the water level would not go up and down, it would just stay in one place and we’d call that “sea level”
Right, another approach is to think about what if the Earth was *almost* locked to the moon. Then surely this bulge would only be slight (rather than collapsing the moment locking occurred). But then that might suggest a 2x or 3x rotating Earth would bulge all the more, but only opposite the moon. This doesn’t really fit in with “the explanation given in class.”
If the earth didn’t rotate vs the moon, the bulges would be bigger because they’d have time to completely flow to where they want to be, but they wouldn’t concern us because they’d be permanent
