[MUSIC PLAYING] As we've seen before on "Space Time," gravity affects the motion of all objects identically.

So if gravity from the Moon and the Sun is really responsible for tides in the ocean and water is water, then why don't we see tides in lakes?

Guess what?

Whatever you believe about why ocean tides exist is probably wrong, even at the most basic level.

In fact, every YouTube video I've ever seen about tides, including ones made by smart people, explains the tides incorrectly.

Typically, they show this diagram, along with an explanation that goes something like this.

The moon's gravity is stronger at Point A and weaker at Point B than it is at Earth's center.

The net effect of this differential of the Moon's gravity across the Earth is to stretch the oceans out like taffy, ergo why the oceans bulge out at opposite points along the Earth/Moon line.

Now, that explanation sounds plausible and a lot of well known scientists give it, but as we'll see, it's not correct.

Don't get me wrong.

The facts are correct.

There really is a gravity differential from the Moon at points A and B.

And at least in this simplified model, there would be two tidal bulges at opposite ends of the Earth/Moon line.

Plus, if Earth could rotate underneath those bulges with no friction between the ocean and Earth's crust, then at a given location on the globe, you would experience two high tides per day as you pass through each bulge and two low tides per day as you pass through the spots at 90 degrees to the bulge.

All of that is true.

What's wrong is the explanation for the bulges.

They aren't actually being lifted or stretched by that gravitational differential.

Something much more subtle is happening that even many professional astronomers and physicists misunderstand-- including me, for many years.

So don't feel bad.

Tides are tricky.

But today, we're going to set the record straight and, in the process, understand how it could be that the ocean has tides, but lakes, bathtubs, and cups of coffee don't.

So right up front, I want to make some assumptions to simplify the analysis and to remove unimportant factors from the picture.

That way, we can better isolate qualitatively what's really causing the tides.

Here we go.

Assumption one-- we're going to use Newtonian gravity.

It's not that Einstein can't explain tides.

He can.

But curved spacetime will only add complexity without actually making things clearer.

Assumption two-- let's ignore the Sun.

For simplicity, we'll focus only on the influence of the Moon.

The Sun's effects are going to work analogously, anyway.

Assumption three-- we're going to pretend the Earth is uniformly covered with one humongous ocean and no continents.

And finally, assumption four-- we're going to pretend that we can switch Earth's gravity on and off whenever we want to.

You got it?

OK. Let's take a closer look at the Moon's gravity differential and how it manifests itself from the perspective of a frame of reference attached to Earth's center.

Forget about the oceans for a minute and just imagine two small blocks, A and B, at opposite ends of the Earth's surface along the Earth/Moon line.

Turn off Earth's gravity.

What happens to the blocks?

Well, relative to a frame out in the ambient space, Block A accelerates toward the Moon more than Earth's center and Earth's center accelerates toward the Moon more than Block B.

So from the perspective of Earth's frame, both blocks will separate from the surface as if acted on by some invisible outward force.

That weird invisible outward force is called the tidal force.

And in Newtonian physics, it's fake.

It's an artifact of Earth's frame of reference.

Remember, Earth itself is accelerating towards the Moon, so according to Newton, Earth's frame is non-inertial.

Now, if you need a refresher on non-inertial frames, you can check out our earlier video on the topic.

But the bottom line is that in Earth's frame, the tidal force looks like anti-gravity, at least along the Earth/Moon line.

And here's the thing.

Just like the fake forces that you perceive in an accelerating train car, tidal forces should make all objects accelerate off the surface identically, regardless of their mass.

An object's resulting acceleration relative to Earth's surface is called the total acceleration of that object, and it should be identical for a pebble and a pony.

But if that's true, the tidal force along the Earth/Moon line can't be raising or stretching the two bulges that lie along that line.

Because if that were the case, then water in lakes should also be lifted and, for that matter, so should sand and rocks and you.

Remember, the object's mass doesn't matter.

Well, we don't see things levitate during high tide.

More important, the math of assuming the bulges are being lifted doesn't work out.

The tidal acceleration on objects due to the Moon's differential gravity along the Earth/Moon line works out to only 1/10,000,000th of an Earth g, and you can't lift something by pulling up on it with a force that's 10 million times smaller than its Earth weight.

Plus, even if you turned Earth's gravity off, you would never notice an outward acceleration of one micron per second per second.

Nevertheless, those bulges in the ocean are real.

So if the ocean isn't being stretched, then how do they get there?

The key is to look at the tidal acceleration of objects that are not on the Earth/Moon line.

For instance, a block at this location is going to be pulled this way by the moon.

But of course, the whole Earth is pulled that way by the Moon, chasing after the block.

So relative to the Earth's surface, the block's tidal acceleration is almost radially inward-- in other words, down.

In fact, if we map out the tidal acceleration vectors that you'd see at different points on Earth's surface, they look like this.

As you can see, tidal forces only act like anti-gravity if you're right on the Earth/Moon line.

At most places, those vectors are largely tangent to Earth's surface, which would push water sideways.

Now, we've drawn these vectors kind of big to help you visualize them.

But in reality, they're microscopic.

Remember, the radially inward acceleration caused by Earth's own gravity on objects is 10 million times bigger.

However, the surface area of the ocean is also enormous, so those tiny tangential sideways pushes on all the chunks of water added up over half the surface of the planet can produce a pretty decent increase in water pressure.

So I think you can start to see what's happening here.

The ocean isn't being lifted or stretched.

Instead, thanks to the cumulative sideways traction everywhere else, it's being squeezed toward the Earth/Moon line and piling up there.

Basically, the moon is turning the entire ocean into a planet sized hydraulic pump and the ocean is bulging along the Earth/Moon line in the same way that a blister or a pimple will bulge up in the center if you start to squeeze it from the side.

So why don't lakes have tides?

Well, largely for the same reason that it's very hard to pop small pimples-- less traction and bad hydraulics.

See, unlike the oceans, a single lake is not a contiguous, planet sized body of water.

Lakes just don't have enough area for the tiny pushes on it to build up enough pressure to change the water level.

Now technically, really big lakes, like Lake Michigan in North America, can generate enough pressure to produce mini tides, maybe with a couple of centimeters difference between low and high tide.

But since winds and boats and aquatic sloshing will all create ripples that are way bigger than that, those mini tides just aren't noticeable.

The same is true for any enclosed body of liquid-- a swimming pool, a bathtub, a human body-- which is basically a big sack of water-- and a cup of coffee technically all experience tides.

They're just microscopic.

Also, remember that Earth itself isn't perfectly rigid.

So when water in a swimming pool rises a tiny amount, Earth's surface is also rising by tiny amount, making the change in water level relative to the surface of the planet even less noticeable.

Now, everything that I've just said is oversimplified, but I think it gets the main point across.

Namely, tides have a lot more in common with pimples than they do with taffy.

OK. We've got a few loose ends to tie up.

First, the Sun-- its effects on tides are analogous to those of the Moon, but they're only about a third as big.

The Sun is more massive, yes, but it's also much further away.

Now, when Earth, the Moon, and the Sun all line up in space, the effects are additive and you get extra-large spring tides.

When, instead, they make a 90 degree angle in space, there's partial cancellation and you get extra small neap tides.

Second, in the simple model of a water world Earth, the math says that the water level should vary by about 3/4 of a meter between high and low tide.

But some places see smaller tides than this while other places, like the Bay of Fundy in Canada, have tidal swings of over 10 meters each day.

So why the variations from place to place?

Well, location relative to the plane of the Moon's orbit is certainly part of it.

But mostly, it's that nooks and crannies in the continents affect the details of how pressure gets distributed through the ocean in non-uniform ways.

For example, some lakes and rivers that have direct ocean inlets do have tides.

But instead of rising gradually, high tide can come in through the inlet like a moving wall of water called the tidal bore, which is pretty cool.

Also, some variation in water level is just sloshing that's not directly related to tides at all.

The bottom line is that the finer details of tides in the real world are just kind of complicated.

Finally, Porscher911, one of our viewers, once asked how Miller's planet in the movie "Interstellar" could've had such a huge waves without the astronauts themselves being stretched or levitated.

I think that other stuff was supposed to be at play there.

But nevertheless, when it comes to liquid on a planet, the squeezing aspect of tidal forces will almost always be more important than the stretching, even in the craziest regions of spacetime.