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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.
So are other things that I haven't mentioned,
like how the rate of Earth's rotation and the ocean tides
affect each other.
For discussions of all of that, I humbly
direct you to other videos and articles that are linked down
in the description.
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.
Last week, we finished our series
on general relativity and curved spacetime.
You guys had a lot of great questions
that I'll address in a second.
But first, a comment about one of our earlier episodes.
A while back, we did an episode clarifying misconceptions
about so-called "habitable" exoplanets.
Now, prior to the airing of that episode,
at the 2015 NASA Space Apps Challenge,
a colleague of mine-- Professor Emily Rice
from the College of Staten Island--
had done a very similar talk about exoplanet atmospheres.
She and I had been talking about exoplanets back and forth
for a while, including in the context of this show,
and there was a lot of overlap between our two talks
that I wasn't aware of at the time that we aired our episode.
If I had been, I would have cited her talk explicitly,
and I'd like to rectify the situation now.
So down in the description, you'll see a link to her talk
about alien atmospheres-- it's very good-- at the NASA Space
Apps Challenge, along with a link to other information
from her website.
Now to your comments.
A lot of you ended up asking very similar questions.
Rather than address your comments individually,
I'm going to address the most frequently
asked questions in bulk.
A lot of you asked about gravitons
in the following context.
You may have heard that in quantum field theory,
forces are described as being mediated
by some kind of particle like electromagnetism
by the photons, strong nuclear forces by the gluon,
and so forth.
So if gravity is not a force and it's
considered spacetime curvature, then why
do people talk about gravitons?
That's an excellent question and it's hard to answer,
but here's the rough bottom line.
Thinking about things in terms of gravitons
and thinking about spacetime curvature
are not necessarily mutually exclusive.
It's just instead of quantizing a sort of standard field,
you're-- that you think of as a force field,
you're quantization something different when you talk about
the quantum version of general relativity.
And it turns out that you can do it self-consistently.
You can quantize any classical theory,
as long as you are restricting yourself
to looking at macroscopic regimes--
large scale things-- and you get pretty good agreement
with general relativity there.
It's when you start looking at very small scales, like what
the quantum version of gravity tells you
on very small scales or very high energies,
that a lot of infinities start popping up in the theory
that you can't get rid of, which is
what we don't have a fully self-consistent, quantized
version of gravity yet.
But from the philosophical perspective
of quantum field theory, you should
be able to quantize anything.
And figuring out how to do that is just still
an unsolved problem in physics.
Related to this question, people ask the converse of it.
Is it possible, then, to geometrize or treat
other forces like electromagnetism
in geometric terms?
Well, that's actually been worked out in some contexts.
You can look up something called Kaluza-Klein theory, which
is a way of trying to get a geometric version
of electromagnetism plus general relativity.
But in general, these are two sort of parallel paradigms.
One is trying to geometrize a lot of stuff,
which was a big thing in the sort of early 20th century.
And the other is to try to take field-- classical field theory
versions of something and then add to them
the machinery of quantum mechanics
to sort of get a quantized version of the world.
And these two things proceed on sort of parallel tracks.
It's hard to answer these things well in 30 seconds
without just throwing out a lot of buzzwords
and giving you what's not really an explanation.
But I don't think there's really any alternative that
wouldn't mislead you.
You're asking very heavy stuff.
A lot of you wanted clarification
on how curvature of time is what's responsible
for, say, circular orbits around the Earth being geodesics.
First, remember that I was speaking very, very loosely.
There's really only spacetime curvature.
You can't really break it up into separate space and time
curvatures.
That doesn't mean anything.
But here's what I did mean.
Suppose that you take a frame attached to Earth's center,
with clocks-- that frame's not going to be inertial--
and then you work out what the equations of general relativity
say the geodesics should be around the Earth
and you down project them into that frame.
So you down project everything into 3D
spatial and temporal terms with respect
to that not inertial frame.
It turns out that the pieces of the geodesic equation--
the things the tell you what the geodesics should
be-- that resemble-- that basically give you
Newton's laws of motion as if there were
a gravitational force-- are just the pieces
of the geodesic equation that involve "time" components when
projected into that frame.
That's really all I meant.
There's actually some good lecture notes by Sean Carroll
that I've linked in the description that
give you a slightly more mathematical treatment of this.
Go up to equation 4.22 in the link that you see below.
A lot of you were expressing confusion
about how two points on Earth's surface
can both be "really" accelerating if Earth's surface
itself is not expanding.
Be careful.
We're using the word acceleration here
in two different and mutually exclusive senses.
In the Newtonian sense, acceleration
would mean put a frame of reference at Earth's center.
Use a clock as if it runs-- pretending
that it runs the same rate everywhere and ask,
relative to that clock, are the coordinate positions
of two points on Earth's surface changing?
And the answer is, of course they're not.
So in that sense, those two points are not accelerating.
But Einstein says, hold on.
In the four-dimensional curved spacetime sense,
you need to give something some kind of inherent, absolute 4D
geometric meaning.
And acceleration in that context means,
is your tangent vector being parallel transported
along your worldline?
For points on Earth's surface, that's not true.
They're not geodesics.
So the way that we have to reconcile things
is, is there a problem with saying
that falling frames, like attached to an apple falling
at both those places, are the ones that we should really
use as the standard, even in the three-dimensional sense,
of non-acceleration.
Einstein says, you don't really have a choice.
You have to do that because it's only the falling frames that
are "purely" non-accelerating in the four-dimensional sense.
The only reason why that seems to conflict
with the idea of using a single frame at Earth's center
and saying that those two points are not accelerating
is that that frame at Earth's center
that you're using the gauge that is not inertial
and so that shouldn't be the standard for saying that things
are not accelerating.
In other words, Einstein says the standard
of non-acceleration can only be defined locally
in small spacetime patches.
If you try to talk about it in any other context,
you're assuming something geometric about the world--
mainly that it is a 3D, Euclidean world that
works the way you think-- you learn
it works in 10th grade that simply isn't true.
Finally, I do want to reference one individual comment.
Iwon't tellmyname was asking what
courses he would need to take to learn about general relativity.
He got some answers from WingedSoda.
And then he replied, OK.
Great.
And I guess I got lots of time because I'm only
going into eighth grade.
That's right.
You got lots of time, Iwon't tellmyname
and you're asking all the right questions.
Keep learning and listening to as much as you can,
even if it doesn't make sense at first.
This stuff takes years to grasp and you're
getting a head start Glad you're watching the show.
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