You are now accelerating: What it means that gravity is not a force (Patreon)

[This is a transcript.]

This video is all about Albert Einstein, yes, that guy again. Einstein is famous for his theory of general relativity. It’s taught us that gravity is not a force. And that’s probably the most misunderstood physics fact, ever. Like, even physicists get it wrong, all the time. Gravity is not a force. And since there’s no force pushing down on you, that means you are currently accelerating upward. Unless you’re watching this from the ISS, in which case please say hi to the moon.

How does gravity work if it’s not a force? That’s what we’ll talk about today.

An accelerometer is a device that measures acceleration. If you’d hold an accelerometer steadily in your hand, it’d tell you it’s accelerated upwards. This isn’t hypothetical, weird theoretical physics talk. You can buy one and just see what it says. This is an example of how the reading of an accelerometer looks like when it’s lying still on a table. It tells you it’s accelerated upwards.

And this is entirely correct. If you hold an accelerometer still on the surface on earth, it’s indeed accelerated upward. Why does that surprise you? If you hold something on your hand you feel that it's pressing against your hand, downward. It’s like when you’re trying to accelerate a car with your hand. It’ll push against it.

If you hold something in your hand, that’s not the gravitational force pushing it down. Because gravity isn’t a force. It’s pushing on your hand because you are accelerating it upward.

Why is the thing in your hand accelerated if you don’t move your hand? It’s because *you are accelerated. And *you are accelerated because there’s a force pushing on you from below. That’s the floor, or rather the atomic bonds in the floor and in the ground below.

You see, the entire earth has internal pressure, otherwise it’d collapse. That pressure generates a force on everything on the surface. And as Newton taught us, a force creates acceleration. So that pressure of Earth creates a force which accelerates you on the surface.

But wait, you may say, there’s also the gravitational force pushing down, so the two forces balance to zero, right? No—oo. Because gravity is not a force.

Gravity is a consequence of moving in a space-time that’s been curved by the presence of masses. If there are no masses nearby to curve space-time, it’s flat. So long as there’s no force acting on an object in this flat space-time, the object will move in a straight line. If there are masses nearby, space-time will curve, and the object no longer move on a straight line, even in the absence of a force.

The usual way to explain this is with a large marble on a rubber sheet, that deforms the rubber. This is an analogy for how, say, a planet curves space-time around it. And then another, smaller marble which seems to be “attracted” to the bigger one. It’s a pretty good visualization, it’s just that you shouldn’t ask why the big marble bends the rubber, then it gets really confusing.

So in this curved space around a planet, if there’s no force acting on you, you fall towards the planet. That’s not an acceleration. But if something gets in your way, like the surface of the planet, then *that creates a force. So now you’re accelerated.

This is why there’s no force pushing down on you right now. There’s only a force pushing up. If you took away the surface of earth, you’d fall. And if you fell, there’d be again no force acting on you.

This is also why the earth would collapse if it had no internal pressure. It’s not because there’s a gravitational force acting on the matter. Because gravity isn’t a force. It’s because without internal pressure, stuff would just freely fall in the curvature that it itself creates. Without internal pressure, earth would form a tiny black hole about 3 mm in diameter and the real estate market would go to hell.

But let’s go back to the accelerometer to see what else they can tell us. The easiest example of an accelerometer is a spring. Yes, a plain boring spring. Suppose you put a spring into outer space, empty space, flat space. How does it get there? I don’t know, maybe Bob the astronaut lost it on a spacewalk? I hear these things happen.

Ok, there’s a spring in outer space for whatever reason. It’ll have some extension. Now if you tie that spring to a rocket and that rocket blasts off, what’s going to happen with the spring? It’ll expand so long as the velocity of the rocket changes. Why is that? Well, as Newton taught us force equals mass times acceleration. So if you accelerate one end of the spring, that creates a force and that force stretches the spring. You can measure how much it stretches, and from that you can calculate how much it was accelerated.

Yeah, I know this isn’t exactly rocket science even if it is, but bear with me for a moment. This example tells us three very important things.

First, you can use a spring to measure acceleration. It’s not the only way to do it, and maybe not even a particularly good one, but works.

Second, you cannot, of course, use the spring to measure the velocity of the rocket, because velocity in and of itself is a meaningless concept. You can only talk about relative velocities, not absolute ones. This is why Einstein’s theories have the word “relative” in them.

This brings us to the third, and most important point that we learn from the spring. Acceleration is not relative, it’s absolute. You can measure how much you’re accelerated, for example with that spring. And you can tell when you are not accelerated.

So we have a spring on a rocket in outer space, alright. What’s this got to do with gravity. Well this is where Einstein’s genius comes in. Einstein said, let’s put the spring in a box from which you can’t look out. You have no idea what’s going on outside. We tie the box with you and the spring to a rocket. The rocket blasts off. What happens? Well, the spring expands again.

Einstein now said that if you’re in the box, you can’t tell whether you’re being accelerated, or whether you are sitting still on the surface of a planet. He then said if there isn’t any measurement that you can do to tell these situations apart, they’re physically indistinguishable. That is, in a small box, the effect of gravity on the surface of a planet is indistinguishable from acceleration in the absence of gravity. This is what’s called the “Equivalence Principle”.

The point where people usually go wrong is to conclude that because gravity is indistinguishable from acceleration, that means gravity accelerates you. But that isn’t so. Because to accelerate something, you need a force. And gravity is not a force. Einstein’s equivalence principle says that you are accelerated if you sit *still in a gravitational field. This is because the only way to sit still in a gravitational field is to have a force acting on you that prevents you from falling. For example, because that floor is pushing on you. But you can’t tell this apart from being accelerated in the absence of gravity, in a flat spacetime.

Imagine for example you are falling into a black hole. No, I don’t mean YouTube recommendations, I mean a literal black hole. You are in a box with your spring and without any rocket boosters and so on. The black hole curves space-time, and you can use the equations of Einstein’s general relativity to calculate what happens. They’ll tell you that if you get too close to the horizon, you’ll inevitably cross it and then you’ll end up in the singularity. Which might not be there, but that’s a different story. The point for today is that your spring won’t budge because there’s no force acting on you. Because gravity is not a force.

This is what physicists mean by “free fall” in a gravitational field. It means there’s no force acting on you, so you’re not accelerated. A zero-g flight is the closest you’ll get to that on earth – at least if you want to survive.

The idea of a zero-g flight is exactly einstein’s elevator experiment. That if you’re in a box whose floor is not pushing on you, that’s the plane, you can’t tell whether you’re in outer space far away from any heavy objects, where space-time is flat, or whether you’re freely falling in a curved space-time. Physically, it’s exactly the same. So the zero-g flight is indeed a good simulation for outer space. And why is that? It’s because gravity is not a force. In the plane, you are falling in a gravitational field, but there’s no force acting on you.

Now, I sometimes hear people say that “zero-g” is a bad term because it suggests that there’s no gravity, but of course the curvature of space-time doesn’t go away just because you sit in a plane.

And that’s right, but zero-g doesn’t mean zero-gravity. The “g” is the local acceleration that you experience if you are in rest in the gravitational field. If you are on the earth’s surface, that acceleration is roughly nine point eight meters per square second, as you probably all learned in kindergarten.  

Though, strictly speaking, this gravitational acceleration isn’t constant. The acceleration that you experience on the surface of earth drops if you go to higher altitudes, and it also slightly depends on what the ground is made of. This is why measuring this acceleration tells you something about the composition of earth’s mantle, but I digress.

To come back to zero-g flights. On a zero-g flight your acceleration is indeed almost zero because you’re not at rest with the surface of earth, that’s why it feels like free fall. Of course it’s not exactly zero, because you always move around somewhat that way or this way, or if you’re Rohin you are doing CPR, but it’s pretty close to zero. So I’d say, zero-g is a good description. Same thing on the ISS.

Okay, but I can see that you’re still confused because you learned that acceleration is a change in velocity. And if you’re not changing velocity, you’re just standing on earth, how can you be accelerated?

Well, the entire point of einstein’s theory of relativity is that velocity is not an absolute. What you mean if you say you’re not changing velocity is that you’re not moving relative to the surface of earth. But this doesn’t mean you have zero velocity, because that’s a meaningless statement. It just means you are not moving relative to something else that’s accelerated the same way, which is the surface of earth.

You can, however, return to talking about Newtonian gravity by re-defining what you mean by “no acceleration”. In general relativity, as we have just seen, you are accelerated if you do not move relative to the surface of the earth, say because you stand on top of a building. If you jump and fall, you are not accelerated because there’s no force acting on you. If you hit the floor, you are very suddenly accelerated again which has, erm, measurable consequences.

In Newtonian gravity, you introduce this new force that you call the gravitational force and say if you’re on top of the building that force of gravity cancels that from the building pushing on you. So now there’s no net force acting on you and Newton says you’re not accelerated. If you jump off the building, Newton would say, the force from below disappears and there’s only the gravitational force acting on you and you’re accelerated. And if you hit the ground, you suddenly return to zero acceleration.

The Newtonian picture is the one we learn at school, and it’s useful so long as you are on earth. But strictly speaking it’s wrong because you can’t just redefine what you mean by zero acceleration. You can’t do that because acceleration it’s not a relativity quantity. If you’re staying in place in a gravitational field, so you are not falling, then you are not at zero acceleration as any accelerometer will tell you.

Now of course physicists are no linguistic saints, and they’ll sometimes refer to gravity as a force even though it isn’t. A typical example is when they speak of the “four fundamental forces of nature”. If they’re being careful though, they’ll refer to it as the “gravitational interaction” and the “four fundamental interactions”. But often they don’t. I think they really just call it a force because that starts with an “F”.

In a nutshell, why is gravity not a force? Because if you are only exposed to the gravitational interaction, you fall, and that is measurably not an acceleration. 

The quiz for this video is here.