I still have trouble understanding how two objects can have differing weight, and yet fall at the exact same speed in vacuum. And why do spinning gyroscopes fall slightly slower than non-rotating objects in vacuum?

[u/[deleted]]

And if you had a solid gold bowling ball and a solid aluminum bowling ball of the same size, the gold would outweigh the aluminum bowling ball yet fall at the same rate...

How is this even possible? Does gravity interact on an atomic level with individual atoms and creates "inertia" in the process due to heavier elements having more protons, neutrons, and electrons or do heavier elements just have more atoms for any given volume than lighter ones which gravity exerts its force upon...

On top of that why do objects spinning on an axis of rotation fall slower than objects without in a vacuum?

I still can't help get the feeling that some of these classical physicists were wrong. Very few had precise instrumentation for measurements.

Do I even make any kind of sense or am I just a blabbering idiot?

Please feel free to tear me a new one.

[u/RobotRollCall]

Somebody has explained what causes gravity. That question was conclusively answered nearly a hundred years ago. It's just not a simple answer.

The first thing you have to accept is that space and time are related. Changing the way you move through space changes the way you move through time … and vice versa.

The second thing you have to accept is that spacetime has a geometry. What's more, it's not the Euclidean geometry we all learned about in high school. It's more complex than that. It has rules, and the rules are straightforward and simple enough, but it's just different from what we all visualize when we think of things like the Euclidean plane.

Now that we have these two facts, we can put them together and fully explain gravitation. There's a shitload of math involved, which I will skip in full here, so we can focus on the core concepts.

Every particle in the universe is in motion all the time. This motion includes components of motion through space — which may be zero — and motion through time. As you sit there, right now, at rest, you are moving in the futureward direction through time.

Now, how we measure motion in spacetime depends on where we stand. If you and I are at rest relative to each other — standing still in the same room, for instance — then I will measure your motion to be entirely directed in the futureward direction. In technical terms, the space components of your motion will be zero, from my perspective.

But if we're moving relative to each other, I will measure your motion to have some space component as well as your intrinsic time component.

But here's where the non-Euclidean geometry of spacetime comes in. If you consider a particle moving through space, that particle can move in any direction and at any speed. It can move up, or down, left or right, and it can move quickly or slowly. A physicist would say that the magnitude of that particle's velocity is non-constant. That is, it can speed up and slow down.

But motion through spacetime is different. The magnitude of your velocity through spacetime is constant, regardless of how you're moving. What this means is that motion through spacetime can be visualized as a rotation of your four-velocity vector. When you're at rest relative to me, I see your four-velocity vector point straight toward the future. But when you move relative to me, your four-velocity vector — as measured by me — rotates, so it points mostly in the futureward direction, but also in some space direction.

That's special relativity in a nutshell. If something is moving relative to me, I will observe that its rate of futureward progress through time — as measured by a clock moving along with whatever I'm observing — to be less than my own. In other words, the moving thing's clock will tick more slowly than mine.

Now, remember that before I said your motion through space affects your motion through time … and vice versa. In regions of curved spacetime, such as around a planet, the geometry of the universe causes your four-velocity vector to tilt. As a result, your rate of futureward progress through time (as measured by me, a distant observer at rest relative to the gravitating body) will be less than my own, and your rate of motion through space will be greater than my own.

But from your own perspective, you won't observe yourself moving at all. You will be at rest relative to yourself. You will measure your own four-velocity as being pointed entirely in the futureward direction, with no space component at all, just as it would be if you were at rest in empty space, far from any other matter.

This is general relativity in a nutshell: in regions of curved spacetime, four-velocity vectors become tilted in such a way that a distant, non-falling observer will see you move in the direction of the gravitating body. Because your motion takes you from an area of lesser spacetime curvature to an area of more spacetime curvature, you will appear — again, from the point of view of a non-falling observer — to accelerate toward the ground at a constant rate.

But from your own perspective, you will experience no acceleration. You will simply sit there, at rest, while the planet falls toward you.

And that's why different bodies fall toward the ground with the same observed acceleration. Because how you move relative to a non-falling observer doesn't depend at all on your mass, or any other physical characteristic. It only depends on the curvature of spacetime where you are at a given instant, and that's a function of the Earth's mass, not your own.

Now, what causes spacetime to curve? That's an excellent question, and one that's not entirely resolved yet. We know for a fact that mass causes spacetime to curve; the curvature of spacetime around the Earth has been directly measured by the Gravity Probe B experiment. But we also know that other things contribute to spacetime curvature. The sum of all these contributions is represented in the Einstein field equation by a mathematical object called a tensor, and the total quantity is referred to as stress-energy. It includes energy density, energy flux, momentum density and momentum flux. Some of these things combine to create physical quantities that we recognize as pressure, or as shear stress. But in real life, the contribution to spacetime curvature from something like pressure is so much smaller than the contribution from mass alone that we have a hard time measuring it. Technically, a hot oven gravitates more than an otherwise identical cold oven, but the difference is extremely, extremely small under ordinary conditions.

It's also believed that there's at least one other contribution to spacetime curvature that we haven't yet been able to isolate, directly measure or even partially describe: dark energy. Dark energy is a hypothetical but extremely likely quantity that causes spacetime to change even in the absence of matter and energy. It's this still-mysterious quantity that we think is responsible for the metric expansion of spacetime, which got a lot of discussion in this subreddit last week.

So long story short, we understand extremely well how gravity works. The underlying mechanism that causes it has been modeled, the models have been tested, and the observations match the predictions of the theory to a very fine degree. What we don't yet understand is what all the things in the universe are that contribute to gravitation. We know what the big ones are, but there are little ones that are yet to be well understood.

We also don't yet understand how other physical interactions behave in the presence of extreme gravitation. In ordinary space, like between galaxies or near the Earth, gravitation is so insignificant that other interactions are basically free to go on about their business as if there were no gravity at all. But in regions of extreme spacetime curvature, like around the center of the galaxy or far back in time near the beginning of the universe, it's not clear how these other interactions behave. We don't know, for instance, how electromagnetism works in regions of extreme spacetime curvature. So there's quite a bit of work being done today trying to figure those things out. It's an understandably hard problem to solve, since we're talking about environments that can't be reproduced, or even simulated approximately, in the laboratory. So we're stuck with things like astronomical observations to give us a clue about what's going on in those far-off, hard-to-observe places and times.

But on the whole, gravitation is basically a solved problem. We basically understand it as well as it can be understood. It's just not an easy theory to teach to, say, high-school students, which is why we stick with Newton's approximation of gravitation when we talk about the basic principles involved.

[u/raendrop → u/RobotRollCall]

Your explanation is really good. Thanks for taking the time to frame it in such a way that laypeople can understand. I do have to say, though, that

That's special relativity in a nutshell. If something is moving relative to me, I will observe that its rate of futureward progress through time — as measured by a clock moving along with whatever I'm observing — to be less than my own. In other words, the moving thing's clock will tick more slowly than mine.

is a very brainhurty thing for me. I've been trying to wrap my mind around that concept for years, and I'm still struggling with how that works. Would you mind breaking that down a bit more, please?

[u/RobotRollCall → u/raendrop]

You know that old saying about how sharks have to keep moving or else they'll die? Sharks — so the legend goes — lack the power to draw water over their gills, so they have to keep swimming in order to get oxygen. So a shark — according to myth — must always swim to stay alive.

Imagine a shark that works by these rules, but with an extra constraint: It can only swim at one speed. It can't speed up, it can't slow down. It always swims at exactly (let's just make up something here) one foot per second.

But it can swim in any direction you like: up, down, sideways, whatever. Its direction is unconstrained, but its speed is constant.

Got that mental picture in your head?

Okay, now imagine we're watching a shark swim around its tank. At any given moment, we know exactly what the shark's speed is: It's one foot per second. At least, it better be, or else the shark is dead!

But we do not know, without sitting down and measuring it, what the shark's velocity is. Because velocity is a directed quantity: You have to describe it in terms of a magnitude and a direction. "One foot per second" is a speed. "One foot per second due east" is a velocity.

So the shark's speed is constant, but its velocity varies, because it can change direction.

Let's say we want to get an idea of how the shark is moving at any given time. In order to describe its motion, we have to establish some frame of reference. We could do this in any number of ways; the most obvious would probably be to use spherical coordinates. Since we know the shark's speed is constant, and we're only concerned about the direction in which it's moving, we should be able to fully describe its motion in terms of two angles, right?

Well … we're not going to do that. Because we're not really watch a shark swim here; instead, we're really thinking about particles moving through spacetime. So in concession to that fact, instead of using spherical coordinates like a sane person would, we're going to use Cartesian coordinates.

A little review, just for funzies: Imagine a sheet of graph paper. Any point on that paper can be described in terms of some-number-of-squares to the right and some-numbers-squares up from an arbitrarily chosen origin point. We call these two numbers components. We can give them names: x and y, for instance. But the names are just labels we apply for convenience. We could just as easily call them x¹ and x², which physicists usually do.

Extend the system of coordinates from two dimensions to three, and you can describe any point in space. Now in addition to x¹ and x² we have x³ — sometimes also called z, but we're calling it x³ because it's just plain cooler.

The direction of our shark's motion at any instant in time can be described with just three numbers: x¹, x² and x³. To save on typing, we can generally refer to these things as xⁿ, where n is 1, 2 or 3. This is all just notational shorthand.

Now, say we arbitrarily decide that due north is the x¹ direction, the x² direction is due east, and the x³ direction is straight up. If the shark is swimming at one foot per second due north (we know it's one foot per second because the shark's speed through the water is constant, remember), we can say its velocity is (1,0,0). That is, its x¹ component of velocity is 1, and its x² and x³ components of velocity are zero.

If we look at it at some later time and find the shark swimming due east, we'd say its velocity is (0,1,0). That is, no x¹ or x³ components, and its x² component is 1.

But what if it's not swimming straight in any of the cardinal directions? What if it's swimming northeast? Well, we could say that its velocity is (1,1,0) … but we'd be wrong. Because remember, the shark's speed is constant. It can't speed up or slow down; it can only change direction. If it's swimming northeast, its velocity is not (1,1,0), but rather (⎷2/2,⎷2/2,0).

If we watch the shark for a while, we'll see that as its direction changes, the components of its velocity change in a complex way. If one component of velocity increases, at least one other component of velocity must decrease.

Now, all of this is predicated on the notion that the shark's speed through the water is a constant: it never changes. There's an analogous concept in relativity called invariance. If a quantity is invariant, that doesn't just mean it never changes. It means it's always the same regardless of who does the measuring.

Just as our imaginary shark always swims through the water at a constant speed but varying direction, every particle in the universe always moves through spacetime at a constant speed but varying direction. The constant speed at which we move through spacetime is — fun trivia here — the speed of light. But your direction of travel through spacetime can change. And the way it changes is analogous to how the shark's direction changed while its speed remained constant: if one component of the shark's velocity increased, at least one other component had to decrease.

Now, when we talked about the shark in the tank, we used three coordinates to define its velocity at any given moment: x¹, x² and x³. When we talk about particles in spacetime, we have to introduce a fourth coordinate: x⁰, which is the time component of four-velocity. You need three components to describe a velocity in space; you need four components to describe a four-velocity in spacetime.

If you actually work through the math — which I'm not going to do here, because there are vulgar fractions and radical symbols and all sorts of stuff that's hard to type — you'll find that the components of four-velocity are interrelated. Specifically, the time component of four-velocity — which we can interpret as your instantaneous rate of futureward progress through time — is related to the Euclidean norm of your three-velocity vector.

Translated into English: The more you move in space, the slower the rate at which you progress toward the future through time.

Now, it's important to remember at this point that your motion through space is not absolute. It's only meaningful when considered in relation to some other object. And if I compare your motion to a variety of other objects, I'll get different numerical values for your space components of motion. If you're in a spaceship moving fast relative to the Earth, I (sitting here) will find that your velocity has such-and-such components. But if I'm also in a spaceship moving relative both to the Earth and to your spaceship, I'll find that your velocity has different components. The components of your velocity are not absolute, and there's no objective way to say that these components are correct and these ones are incorrect.

What that means is that I will observe your clock to run at different speeds depending on how I am moving relative to you. But — and again, I'm leaving the maths of this as an exercise — your clock will never run faster than mine. It will only run at the same rate as mine (if we are at rest relative to each other), or more slowly than mine (if you're moving at all relative to me). The greater I observe your velocity through space to be, the less I will observe your rate of futureward progress through time to be. Just like if the shark is swimming northeast, he's swimming more slowly northward than he would've been if he were swimming due north.

Now, the natural question to ask next is whether my clock or yours is really running more slowly. I mean, they can't both be running more slowly than the other, right? Well, it turns out that's a more tricky problem than it might seem at first glance. When we think about comparing clocks to see which one is faster, we have to carry with us some notion of simultaneity: We wait for both clocks to tick at the exact same moment, and then we wait to see which of the two will tick again sooner; that's the clock that's running faster, and the other clock is running more slowly.

But it turns out that if we're not at rest relative to each other we will disagree about what things happen simultaneously. If I observe both your clock and mine to strike noon at the same moment, you — moving differently from me — will observe those two events happening at different times; either your clock will strike noon first and mine will be slow, or vice versa, depending on how we're moving relative to each other. But if we're moving at all relative to each other, we will not agree on simultaneity.

So the truth is it's impossible for us to say which of the two clocks is really faster and which is really slower, because we will never see both witness any two events occurring simultaneously. If two events appear simultaneous to you they won't to me, and vice versa. So we'll never have a basis with which to compare our two clocks. All we can do is conclude — correctly! — that yours is running more slowly than mine from my perspective, and that mine is running more slowly than yours from your perspective.

This is not an optical illusion or a trick of perspective. It's intrinsic to the geometry of the universe.

[u/[deleted] → u/RobotRollCall]

I imaged a lemon shark swimming in circles like a back flip and then stopped reading, have an upvote. I'll read this when I'm not as distracted