Video Which Way Is Down?

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26:10   |   Nov 02, 2017


Which Way Is Down?
Which Way Is Down? thumb Which Way Is Down? thumb Which Way Is Down? thumb


  • Hey, Vsauce. Michael here.
  • Down here.
  • But which way is down?
  • And how much does down weigh? Well, down weighs about a 100th of a gram per cubic centimeter.
  • It is light and airy, which makes it a great source of insulation and buoyancy for water birds.
  • But if you let go of down...
  • It falls down.
  • So that's which way down is.
  • It's the direction gravity is pulling everything in.
  • Now, for someone on the other side of the Earth, my down is their up.
  • But where are falling things going? Why do things fall?
  • Are they being pushed, or pulled, or is it because of time travel?
  • First things first: let's turn the Sun into a black hole.
  • We can do that using Universe Sandbox 2, this simulator will blow your mind. I love it.
  • In fact, I love it so much I put a code to get the game for free in the current Curiosity Box.
  • If you're not subscribed to the box yet, you are missing out!
  • Okay, look, for the purposes of this video, we want the Solar System.
  • And here it is. Notice that everything's moving pretty quickly around the Sun.
  • That's because we currently have the game set so that every second that passes for us,
  • is 14 days, almost, in the game.
  • If I change this to one second,
  • we're looking at the Solar System in real time.
  • You'll notice that it almost looks like it's frozen.
  • Even though the earth is traveling around the Sun at about 30 km/s, it barely appears to be moving.
  • That is how vast space is. Anyway, let's go back to 14 days
  • I like that motion. Now look at the Sun
  • It is not, currently, a black hole, but we can change that. What we need to do is compress the Sun.
  • So let's lock its mass so that it doesn't change while we make its radius smaller.
  • Let's make its radius as small as we can.
  • And, oh, where'd it go? Well it's still there, it's just become a black hole.
  • Pretty spooky, but now, let's look at the rest of the Solar System.
  • Alright, zooming out and-
  • huh.
  • Nothing's... changed. I mean something's changed.
  • It's colder and darker, but nothing's flying off into space or getting sucked in.
  • You see, by shrinking the Sun, we didn't change the direction of down for the planets.
  • They're always being pulled by gravity towards its middle and making it smaller didn't move where the middle was.
  • But also, the strength of that force pulling them to the middle of the sun stayed the same.
  • That gives us a clue as to what down is.
  • The clue is the other thing we didn't change: mass.
  • Mass is a measure of how hard it is to accelerate something; to change its motion.
  • Now right now, these two balls have zero motion relative to me.
  • Slapping around this hollow plastic ball
  • is pretty easy, but doing the same to this solid steel ball
  • is a lot harder.
  • Now gravity and weight have nothing to do with this.
  • Gravity acts downward, not against my horizontal slapping.
  • Of course, gravity does contribute to friction, but friction works against me when I start moving the ball,
  • but works with me when I stop the ball.
  • And the steel ball is harder to stop than the plastic ball.
  • The difference is mass. The steel ball is more massive
  • It's more resistant to having its motion changed.
  • Mass is an intrinsic property; it does not depend on what's around or change from place to place.
  • It can sometimes be thought of as the amount of matter something has.
  • Your mass is the same regardless of where you are.
  • On the moon, on earth, in the middle of intergalactic space floating around.
  • But all of this said, mass does seem to care about what's around.
  • Mass loves company.
  • Things with mass and/or energy are attracted together by a force that we call gravity.
  • The feeling of gravity is just you and the earth being attracted to one another.
  • Now every portion of an object with mass attracts other portions towards it.
  • The average of all this pulling is an attraction between centers of mass.
  • Giant things like Earth exert an obvious pull, but everything does. Even a baseball.
  • These two baseballs are attracted together by their own gravities.
  • Except their masses are so small, the force is minuscule, and it can't overcome friction or push air out of the way.
  • They're never gonna come together
  • But if you put two baseballs one meter apart in the middle of empty space where no other forces could act on them
  • They would literally fall together and collide.
  • It would take three days to happen, but it would.
  • Isaac Newton found that the strength of the force bringing two things together is equal to the product of their masses
  • Divided by the distance between their centers of mass squared times big G, the gravitational constant.
  • If you make one of two objects more massive, or move them closer together, the force will be
  • stronger and this force of attraction is what we call weight
  • So mass is intrinsic, whereas weight depends on what's around.
  • Now, a weird thing happens when you weigh yourself on most scales.
  • Weight is a force, but scales display pounds or kilograms,
  • which are units of mass.
  • What's going on is that a scale is
  • activated by a force.
  • Any force.
  • It doesn't have to be caused by gravity. The scale then displays what amount of mass
  • near the surface of the earth would be attracted to the earth with the force it's detecting.
  • Now since scales tend to be used on the surface of the earth, by people, on which the only force acting is gravity,
  • they tend to not be very far off. But they can be easily tricked, and they further lead to the confusion between mass and weight.
  • Notice that weight is mutual. You are pulled down by earth with the same force that you pull up on earth.
  • According to a scale, I weigh
  • 180 pounds on earth..
  • And the earth weighs 180 pounds on me.
  • But because the Earth's mass is so much greater than my own, and
  • because the more massive something is, the more it resists being moved, our
  • equal and opposite weight forces accelerate me a lot more than the earth.
  • If you drop a pencil from a height of 6 feet, the pencil doesn't just fall to the earth. More precisely,
  • they both come together.
  • They're attracted to each other by equal forces
  • but the same force moves the pencil a
  • lot more than the earth. When you let go of the pencil, the earth is literally pulled up
  • to the pencil by the pencil's own gravity, a distance equal to about 9 trillionths
  • the width of a proton. That
  • same force moves the pencil the remaining distance, which is still pretty much six feet.
  • At the height of the International Space Station's orbit, you and earth are attracted about
  • 10% less than when you're on the surface; about eight point eight times your mass, but not zero.
  • For this reason, weightless astronauts in zero gravity are neither weightless, nor in zero gravity.
  • Their weight force fails to bring them and earth together, because they move horizontally
  • so quickly that they fall just as fast as Earth's surface curves away from them.
  • And even though they're experiencing 90 percent of the gravity you and I are feeling right now,
  • (That's why they don't just fly away)
  • There are no forces, called g-forces, to resist their weight, since everything around them is falling too.
  • It's resistance to your weight force, stress,
  • deformation, that is needed for you to feel weight. What astronauts in orbit actually lack is
  • apparent weight.
  • Likewise, a helium balloon has weight.
  • I mean, it's made out of matter it clearly has mass, so it's attracted to the earth.
  • Let's try to measure its weight force.
  • Okay, it has negative apparent weight.
  • That's because its attraction to the earth is weaker than the buoyant forces from the air around it that push it up.
  • Now, while it moves up,
  • It pushes air molecules down, but they transfer that force widely. Not just directly down onto the scale.
  • Buoyant forces are caused by the fact that whenever you are immersed in a fluid like water or air,
  • molecules lower down are at greater pressure.
  • They're being pressed by the weight of all the molecules
  • above them and are closer to earth, so they're pulled to it with a stronger force. Now having greater pressure
  • means they pack a bigger punch when they collide with things.
  • So,
  • horizontally, those collisions cancel out,
  • but vertically, the stronger collisions from below win out, providing lift, a buoyant force.
  • This even happens on your own body. Across its surface area air lifts you with the force of about one
  • Newton, which is equal to the weight force of an apple. So if you weighed yourself in a vacuum you would weigh about
  • this much more.
  • But that's not all Earth's spin causes it to bulge at the equator so the closer you are to it
  • The further you are from Earth's center of mass and the less your actual gravitational weight will be down is
  • Always changing, I mean
  • where is Earth's center of mass? It would always be the same as Earth's geometric middle if Earth's
  • composition was uniform, but earth contains pockets of massive rock at different depths water mountains
  • It's got moving changing insides and air and seasonal ice and though they're far away
  • Gravity extends forever from everything so the moon the Sun the planets all of them pull on you
  • negligibly,
  • But truly. You weigh about a millionth of your weight less when the moon is directly above you
  • This chunky shifting balance of material on earth and ever where else in the universe means that down is
  • always
  • changing on top of that Earth's spin
  • Skews what you consider the direction of down away from its center of mass because the push you get from Earth's spin
  • Seems to slightly lift you reducing your apparent weight and bending down
  • towards the equator
  • The net result is an apparent weight reduction at the equator of about half of a percent if a scale guesses your mass must be
  • 200 pounds at the poles it'll guess that you're
  • 199 at the equator. The 9.8
  • Multiplier used so often in physics is calculated based on how these factors affect someone at 45 degrees latitude
  • all of these influences on the direction of down result in a total vertical deflection.
  • That's only ever at most a few arc seconds anywhere on earth
  • That's not enough to be felt, but changes in direction and strength can be used to study the shape of the seafloor
  • Determine what's under you or even help you discover ancient buried rooms?
  • Point is all of our downs aren't a bunch of radially symmetric lines
  • Down is an uncombed mess.
  • Now since solids don't flow they can have shapes that don't pay much mind to this but water can
  • Flow so ignoring influences like wind and tides the surface of oceans and lakes and puddles is always perpendicular
  • To down if water could pass through land, or if earth were submerged in water
  • Gravity would be the same everywhere along its bumpy surface
  • Such a surface is called a geoid and can be drawn at any altitude
  • If you wanted to build a table that completely enclosed the earth it would have to have rolling undulation
  • Z' nearly 100 meters at some points in order to be
  • Level so that a ball placed anywhere on it wouldn't roll
  • Here is Earth's G. I exaggerated a thousand times
  • You'd weigh about a hundredth of a percent less a few grams here?
  • Then you would say here where gravity is a bit stronger point is the strength and direction
  • Down is variable by location and changes over time
  • So down is a fluctuating vector easy enough except?
  • Why should matter attract matter in the first place?
  • Isaac Newton was able to describe attraction, but not explain it
  • humanity got closer however when Albert Einstein introduced his general theory of relativity
  • Einstein thought a lot about the fact that everything falls to the ground
  • At the same rate no matter
  • How massive something is when dropped it will accelerate towards the earth down gaining about 9.8
  • Meters per second for every second that it falls. That means that a hammer
  • That's quite massive, and a not so massive feather when dropped from the same height will hit the ground at the same time
  • Okay, what just happened...
  • was an "air"ror.
  • awkward laugh
  • In order to fall through air a thing has to push air out of the way
  • But if it has a large surface area and a low weight force it will have a lot of air to move
  • But won't be able to move that air very quickly. In a vacuum, things do fall at the same rate regardless
  • Of mass. This was famously demonstrated by Apollo 15 commander David Scott on the moon
  • And I'll, uh, drop the two of them here and hopefully, they'll hit the ground at the same time.
  • How 'bout that?
  • That's weird right? I mean if a more massive object is pulled with a greater force
  • Shouldn't it fall faster? Well Newton's explanation was simple:
  • Larger masses are attracted with greater forces
  • But will also require more force to be accelerated the same as a less massive thing
  • Something a hundred times more massive might require a hundred times the force, but it will be pulled by gravity
  • 100 times more so everything falls to earth at the same rate
  • What a fun coincidence right?
  • Maybe not
  • Einstein realized that there's another way for things to appear to fall together
  • of their masses
  • Imagine a feather and a hammer floating in space in a room if the room is suddenly accelerated up at 9.8
  • M/s^2 the feather and the hammer will hit the floor at the same time
  • furthermore whether it's the room coming up to meet them or gravity being suddenly switched on
  • Neither object will feel any force pushing them
  • There's no way to tell which of these happen. This is Einstein's famous
  • equivalence principle
  • He once admitted that his greatest thought ever was that of a man
  • falling off of a roof
  • While falling the man would not feel any forces on him even though. He's speeding up
  • freefall is
  • Indistinguishable from floating alone in space from having no forces on you from not being moved
  • What if gravity isn't a force at all what if things fall not because they're being pushed or pulled
  • But because they're not being pushed or pull
  • To see how this could be we need to talk about straight lines
  • What I have here is a retractable ID badge holder
  • This is a great way to test for straight paths
  • Because the string is always kept taut the card
  • I have behind has two lines drawn on it
  • And if while I pull the string out it always stays between those two lines
  • I will know that I never turned
  • While I pulled it because any turn will translate into a different angle between the lines on the card and the string
  • Now if I put two of these on a flat table and pull them out, always ensuring that they go straight ahead
  • They will never meet. They will be forever parallel, but now let's put them on a sphere a curved surface
  • Again, I pull both strings forward making sure that they always are pulled out straight. No turning
  • Wait they came together
  • Well, they didn't turn look
  • Maybe there's some kind of weird force that pulled my hands together and just like gravity. I didn't feel it, but it happened
  • No
  • What happened was not the result of a force it was just a natural result of?
  • Curvature you might be thinking wait a second are those really straight lines. I mean they don't look that straight to me
  • Also, what if they've just moved along latitude lines then they've never come together and those look pretty darn straight
  • But they're not a straight line never turns and although latitude lines look straight at first glance
  • following one requires
  • Turning to find straight line paths on surfaces whether they're flat like this or curved
  • I love the ribbon test. Now you can use an actual ribbon
  • But I have found that a strip of paper works. Even better. Let's take a look at this path right here
  • It's straight at first, but then it curves now if two people are traveling along this curve
  • And they want to stay together the person on the inside will have to cover a shorter distance than the person on the outside
  • Since both sides of this strip of paper cannot change their lengths
  • They'll help us find a straight path if the strip of paper can lay flat
  • We'll know that we have found a straight line and as you can see
  • The strip can lay flat and follow the straight part of this path
  • But when it comes to the curve in order to follow the path now
  • The strip well it has too much material on the inside and that material
  • Bunches up and leaves the plane therefore we know that this part of the path is not straight
  • Let's use the ribbon test to find straight lines on the surface of a cone
  • Well from the looks of it aligned directly from the base to the tip seems like it would be straight and sure enough
  • Yeah, the ribbon lays flat on that path, but what about a ring around the cone?
  • Nope doesn't work shorter distances around nearer the tip of the cone mean that there's too much ribbon up at the top
  • So doesn't lay flat
  • Let's see what else is there though besides this well if I start here and just allow the ribbon
  • to lay flat
  • Huh I get a little curvy looking shape like this
  • I say curvy looking because while to someone say at the base this path might seem to go up
  • Slow down change direction and then fall down faster and faster since a ribbon on such a path is flat
  • It's actually for inhabitants on the cones surface
  • Perfectly straight if we trace the ribbons path on to the cone
  • We can see this clearly because a cone can be flattened a straight line on a curved surface is called a geodesic
  • Here is a geodesic on a sphere the Equator is one
  • Here's another a line of latitude is not a geodesic
  • It's not a straight line to see why let's try to follow it with the ribbon you
  • Know what I have to keep kind of lifting it
  • Yeah, see distances around the sphere becomes shorter as we go up
  • So there's too much material on the ribbon up here
  • and it leaves the surface this path contains turns and in order to turn a
  • Force has to act on you if no forces
  • Did this is the path you would take notice that the ribbon begins moving due east, but then falls
  • south
  • Falls
  • Einstein realized that curvature could cause things to be seemingly attracted to one another
  • Without needing to invent the existence of forces like gravity
  • but attraction only happens if things move along the surface if they stay still they
  • Well, they don't come together so for something at rest. How does falling begin?
  • I mean the thing has to move in this direction, but it's at rest right well
  • Yes
  • But it's only at rest in space and that's not the whole story up down
  • Forward backward and left-right are all you need to describe where an event occur but a complete description will also need to describe
  • When together these four dimensions form the setting in which everything in our universe happens
  • Space-time
  • Since we can talk about a falling pencil using just one spatial dimension up and down we can use a piece of paper to model
  • Space-time for it. Okay, so we've got up and down, but we have to add another
  • direction the pencil moves in
  • time
  • Now if no forces act on the pencil it won't move through space
  • It will only get older and as you can see if all it does is get older
  • It won't fall if space-time was flat when I let go of the pencil
  • it wouldn't go anywhere, but now let's allow the earth which is massive to manipulate space-time into say a
  • cone
  • Now with no forces acting on it every part of the pencil follows a straight line
  • But on a cone as we saw earlier such a path will look like this it will fall
  • This is because distances around the cone are shorter higher up
  • Time runs faster further from a massive object, but to go straight
  • Not turn every part of the pencil must cover an equal distance in space-time
  • like this
  • Only when the pencil hits the earth does the repulsion of their mutual electrons provide a force pushing the pencil off a geodesic
  • For the earth time is a series of slices from this evolution the pencils force-free
  • Geodesic is why it falls not a push or pull just the pencils natural tendency to follow a straight line
  • Until something acts on it now. We only used one dimension of space and one of time because
  • Visualizing our universes three of space and one of time would take us beyond the limits of what could be shown on paper or screens
  • but math
  • Can take us there
  • General relativity allows us to calculate how much mass and energy
  • Curved space-time and has been used to explain things that Newton's older theory of falling as the result of
  • Forces couldn't like anomalies in the orbit of mercury which orbits nearest the Sun and is therefore most affected by the sun's grip on
  • space-time many other experiments have confirmed general relativity's picture of the universe fitting the conclusion that
  • There is no
  • Gravity there's just
  • Space-time its curvature and a us in it. As John Wheeler famously put it
  • Space-time grips mass telling it how to move mass grips space-time telling it how to curve?
  • Relative to the earth we don't move very fast even jet airplanes move negligibly close to the speed of light
  • So relative to earth we move almost
  • Exclusively through time as such we are more affected by the way time is curved by mass
  • Than how space is curved?
  • This has led many to claim that for the most part you feel as though you're being pushed into the ground
  • Not because of a force called gravity
  • But because time is moving faster for your head than for your feet down is
  • Relative and always changing, but it exists because of and is always in the direction of slower time
  • Bertrand Russell called this the law of cosmic laziness
  • Everything is naturally steered towards where time is slowest we call this falling
  • going down
  • So you don't have to keep anything on the down-low
  • time will take care of that for you and
  • and as always
  • Thanks for watching
  • Remember that you can support Vsauce and Alzheimer's research by subscribing to the Vsauce
  • curiosity box the current one comes with a code to get a free copy of universe sandbox 2
  • Which is amazing and a whole host of other science toys and tools picked by myself Jake and Kevin
  • I love it all so I hope to see you at brain candy live. We are coming to many many cities very soon
  • Hopefully one near you by going to the show you can see Adam
  • And I doing things that will you may not have seen us do before we also explore the science and common
  • misconceptions behind all things
  • Err. Maybe have said too much. Maybe not I hope to see you there and as always thanks for watching

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BRAIN CANDY LIVE http://www.braincandylive.com/tickets
THE VSAUCE CURIOSITY BOX: https://www.curiositybox.com/
Links to sources and to learn more below!

my twitter https://twitter.com/tweetsauce
my instagram https://www.instagram.com/electricpants

Thanks to Eric Langlay (https://www.youtube.com/user/ericdraven30) for producing, editing, and animating this episode with me. Thanks also to Henry Reich (https://www.youtube.com/user/minutephysics) for his advice and guidance.

Universe Sandbox² : http://universesandbox.com/

Mass vs weight:

Great Veritasium video: /watch?v=_Z0X0yE8Ioc
two other great videos: /watch?v=6ccIjRwYO9U and /watch?v=aCqQzrPCcFM

baseballs coming together under gravitational attraction can be simulated in Universe Sandbox 2. More math behind it can be found here: https://www.reddit.com/r/explainlikeimfive/comments/2vyxl7/eli5_will_two_baseballs_a_foot_apart_in_deep/

Weight to mass (on surface of Earth) convertor: https://www.convertunits.com/from/kilograms/to/newton

pencil and Earth falling numbers: https://www.quora.com/When-we-drop-a-pencil-the-earth-attracts-it-and-it-seems-that-the-pencil-is-falling-towards-earth-Why-doesnt-the-earth-come-up-towards-the-pencil

NASA HD footage: https://archive.org/details/NASA-Ultra-High-Definition

Buoyancy: https://en.wikipedia.org/wiki/Buoyancy

Earth’s spin and its effect on ‘down’: http://www.freemars.org/jeff/Earth/down.htm

The measurement of Earth and its gravity:


Movement of Earth’s center of mass:


you get heavier before you get lighter as you descend into Earth: https://www.reddit.com/r/askscience/comments/4qfl52/do_you_get_lighter_the_further_underground_that/

vertical deflection:


practical uses of measuring gravity: https://en.wikipedia.org/wiki/Gravimetry



Interactive Earth geoid: https://experiments.withgoogle.com/chrome/geoid-viewer

your weight when moon is overhead: https://www.thenakedscientists.com/forum/index.php?topic=11639.0

Hammer and feather drop on moon: https://nssdc.gsfc.nasa.gov/planetary/lunar/apollo_15_feather_drop.html

Why things fall at the same rate: https://www.quora.com/If-an-object-has-more-mass-then-its-pull-on-earth-would-be-greater-than-an-object-with-less-mass-and-therefore-should-fall-to-earth-faster-Why-do-objects-of-different-mass-fall-to-earth-at-the-same-speed

Wolfram Alpha cone geodesic tool: http://demonstrations.wolfram.com/ConeGeodesics/

General Relativity:

simple animation showing geodesic on cone and how it causes motion DOWN in space: /watch?v=DdC0QN6f3G4
GREAT pbs spacetime video (watch the whole channel): /watch?v=AwhKZ3fd9JA

time and gravity:


tests of general relativity: https://en.wikipedia.org/wiki/Tests_of_general_relativity


great introductory texts:

“Relativity Visualized” by Lewis Carroll Epstein https://www.amazon.com/Relativity-Explained-Classics-Science-Mathematics/dp/0486293157

There’s also this PDF that takes Epstein’s diagrams into more detail: http://www.relativity.li/uploads/pdf/English/Epstein_en.pdf

“Relativity Simply Explained” by Martin Gardener https://www.amazon.com/Relativity-Explained-Classics-Science-Mathematics/dp/0486293157

great intro to the math of general relativity:

“A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity” by Peter Collier https://www.amazon.com/Most-Incomprehensible-Thing-Introduction-Mathematics/dp/0957389469/

Requires some background in relevant math topics (see above) but very very good:

“Spacetime And Geometry: An Introduction To General Relativity” by Sean Carrol https://www.amazon.com/gp/product/9332571651/

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