This video explains Albert Einstein's General Theory of Relativity, which posits that gravity is not a force but an effect of spacetime curvature. It uses analogies like falling men and rockets to illustrate the equivalence principle and how objects follow geodesics (straightest possible paths) through curved spacetime. The video also touches upon the classical mystery of why all objects fall at the same rate and how general relativity resolves this, along with an experimental test involving light bending around the sun.
According to the general theory of relativity, gravity is not a force. There are no gravitational fields. Gravity is kind of an illusion, and in this video, I will prove it to you by blasting off into outer space.
Albert Einstein said the happiest thought of his life was imagining a man falling off the roof of a house. What made Einstein so happy about this was not some freudian slip, it was the realization that this man, while he was falling, would not feel his own weight. He would be weightless. And anything he dropped on his way down, well, it would remain stationary relative to him or moving in uniform motion. The whole situation would be just like if you were in deep space, not near any large masses, with your spaceship at rest or coasting along at constant velocity. Here, you would feel no weight. Objects would remain stationary relative to you, or if you give them a push, they would move in a straight line at constant velocity. And you would be the very definition of an inertial observer. You're not accelerating, not in a gravitational field. All the laws of physics apply in your reference frame, meaning there is no experiment you could do to distinguish your inertial reference frame from any other.
Now here comes the big leap. Einstein looks at these two scenarios and says they are equivalent, not just similar. Physically, they are exactly the same thing. Which means, man falling from roof is not in a gravitational field. There are no gravitational fields. And he is not accelerating. He is an inertial observer, just like rocket man. Whoa, whoa, whoa. I mean, okay, I can see how both of these observers feel weightless. But a man falling from a roof is clearly in a gravitational field. I mean, he's right next to the earth and he's obviously accelerating. His speed is increasing by 9.8 meters per second every second, a fact that will become painfully apparent when he crashes into the ground.
I know that these two situations look very different, but Einstein's equivalence principle tells us the one thing to focus on: the experience of the observer. If they feel weightless, then they are in an inertial frame of reference, every bit as good as rocket man's out drifting through deep space. Imagine if rocket man, coasting along at constant velocity, and not paying attention, comes upon a planet a long way off in the distance. An external observer might notice that the path of the rocket bends ever so slightly towards the planet. But inside, rocket man would remain oblivious. He feels no force, experiences no acceleration. As the rocket gets closer to the planet, it goes faster and faster. But rocket man still feels weightless. For him, nothing has changed. So where on this journey would you say the frame of reference changes from inertial to non-inertial? An on-board accelerometer would never even register a blip. He has continued on his inertial path through space-time. So the logical conclusion is his frame of reference is inertial up until the instant he crashes into the planet.
Okay, so how do you explain the curved path of his rocket without gravitational forces or gravitational fields? The answer is curved spacetime. First, focus on rocket man's observation that the whole time, he felt like he was moving with constant velocity in a straight line. He was moving in a straight line through space-time. But spacetime around massive objects like planets is curved. So that's why his path appeared curved to a distant observer. Now, this isn't as unusual as it seems. Airplanes, for example, always try to fly the shortest route between cities. Essentially, they just go in a straight line. But since the earth's surface is curved, the shortest path doesn't look like a straight line. These shortest paths over curved surfaces are called geodesics. And we use that same word, geodesics, for the straight line paths followed by inertial observers through curved spacetime.
Here's another analogy. Imagine you and a friend are standing a thousand kilometers apart on the equator. Now you both set off due north. Over time, you will come closer together, ultimately bumping into each other at the North Pole. It's as though there was a force pushing you together. But you didn't feel a force, and your friend didn't feel a force. Gravity is just like that. Gravity doesn't actually exist. The real reason for you coming together was that you were both on straight paths, geodesics, on a curved surface. Astronauts on the space station are weightless. That means they too are inertial observers traveling on a geodesic. But the Earth curves spacetime around it, which is why their straight-line path appears as a helix. It only looks like a circular orbit if you forget the time dimension. Don't forget, we are all moving through space and time. Space time.
This is the standard bent sheet analogy for curved spacetime. But I think this demo is misleading. It allows you to fool yourself into thinking you understand General Relativity when the intuition you're actually drawing on is just that objects like to fall towards the middle of a well due to the gravitational force. But in General Relativity, there is no gravitational force. What you should be thinking about is objects traveling on a straight line path through spacetime. It just so happens that spacetime is curved around massive objects, so that straight line path doesn't look like a straight line. "Matter tells spacetime how to curve, and spacetime tells matter how to move."
Now let's go back to deep space. What happens if you turn on the rocket thrusters and accelerate at 9.8 meters per second squared? Well, someone outside would see all objects remain stationary while the floor of the rocket accelerates into them. Inside the rocket, everything would appear to accelerate down to the ground, and you would feel a force pushing up on your feet. The same force that's pushing up on you as you watch this video. This situation feels exactly the same as being at rest on the surface of Earth. Because we are at rest on the surface of Earth. Now, I want to ask you, are you watching this video in an inertial frame of reference? Well, I mean, do you feel weightless? No. So you are not an inertial observer. Your situation is exactly the same as someone accelerating on a rocket ship in deep space. And let me be clear, I don't mean that being at rest in a gravitational field is like accelerating in a rocket. I mean it is the exact same thing. You are accelerating, and there is no gravitational field. Gravitational fields do not exist.
Now, I know that sounds crazy, but come with me for a minute. This is you in standard Newtonian physics. We draw your weight force, the force of gravity pushing you down, and the normal force from the floor pushing you up. We say these forces are equal and opposite, so there's no net force on you, so you are not accelerating. But in General Relativity, gravity is not a force. You have no weight. So the only force on you are these normal forces pushing you up. So you are accelerating upwards. But I'm not moving up. Relative to what? Relative to the flip chart and the floor and basically everything in this room. But all of those things are in your frame of reference, which you know is not inertial. Relative to everything in my rocket ship, I'm not accelerating. What you need, if you really want to measure your acceleration, is someone in an inertial frame of reference, like the guy who fell off the roof. And he would see you accelerating up at 9.8 meters per second squared. I think what this shows is that what an acceleration really is, is it's a deviation from a geodesic. You can't follow a straight-line path through spacetime because the floor prevents you from doing that. It applies a force upwards on you.
So you're accelerating up. But if I'm accelerating up, and so is everyone else around the world, and presumably the whole surface of the Earth, then shouldn't the Earth be expanding? No. It is possible for you to be accelerating even though your spatial coordinates are not changing. I will show you one equation from General Relativity. This says that the second derivative of your position with respect to time is equal to your acceleration. That's just F on M. And if you were in flat spacetime, well, this is exactly what you're saying. If you're accelerating, your spatial coordinates have to change. But you're not in flat spacetime. And this term is related to the curvature of spacetime. And this is your velocity through time squared. You don't have to worry about the details here. The point is, your position can be not changing. This can be zero, which means your acceleration must be exactly equal to this curvature term times your velocity through time squared. So in curved spacetime, you need to accelerate just to stand still.
A lot of this may seem more complicated than Newtonian physics, but one classical mystery looks a whole lot simpler in General Relativity, which is why all objects fall at the same rate. Now, I have made a number of videos on this topic, and I would always give the standard Newtonian explanation: the only force on a free-falling body is its weight, GMM on R squared, which equals its mass times acceleration. You can cancel the object's mass on both sides of the equation. Hence, all objects will have this same acceleration. The mystery is why we could cancel these two M's. The one on the left was gravitational mass, the property of an object that creates and experiences a gravitational field, while the M on the right is inertial mass, a measure of resistance to acceleration. Why should these two conceptually different properties be numerically identical? Scientists have spent a lot of time and effort experimentally testing down to around one part in 10 trillion that these two types of mass really are the same. But in General Relativity, there is no mystery. All objects appear to fall the same way because they're not accelerating. They're just following straight-line paths through spacetime until they encounter something that stops them. Like the objects in the rocket ship. They appear to accelerate at the same rate because they're not really accelerating. It's the floor accelerating into them.
Now, a lot of this might seem pretty far-fetched, as it did back in 1915 when Einstein proposed it. So he very cleverly came up with a measurable prediction that scientists could make to test his theory. Imagine that this rocket ship is coasting through deep space. If you shine a light beam across the rocket ship, well, it'll do exactly what you expect. Light travels in a straight line and hits a point on the opposite wall at exactly the same height as the source. But now, what if this rocket is accelerating? Well, to an external observer, they're still going to see the same thing: light traveling in a straight line. But inside the rocket, during the time it takes for the light to travel across the cabin, the rocket will have sped up. So by the time it hits the other wall, it'll hit a little lower than before. So in an accelerating frame of reference, light deflects down. Here, I am dramatically exaggerating the effect. Even if I were accelerating up at 10 G's, which would probably kill me, the deflection would be on the order of the width of a proton. Still, it shows that an accelerating frame of reference will bend light.
So Einstein reasoned, light must also bend when it passes a large mass. But where do you find a mass large enough? Well, the only obvious huge mass near the Earth is the Sun. So the ideal experiment would be to look at light passing just next to the Sun and see if it is deflected. Say, light from distant stars. The problem was, of course, the Sun is just so bright, you can't see stars right next to it unless there is a total solar eclipse. Which is exactly what happened in 1919. So Arthur Eddington set out to take pictures of the stars right next to the Sun during totality. And what he found by analyzing those pictures was that their positions appeared deflected by the precise amount predicted by Einstein's General Theory of Relativity. The result was twice the deflection some had calculated using a strictly Newtonian model.
In General Relativity has passed virtually every test put to it over the past hundred years or so. But there are still more things to try. A well-known and empirically validated finding is that accelerating charges radiate electromagnetic radiation. So one conceptually simple experimental test would be to compare the behavior of a stationary charge in a gravitational field to a free-falling one. If a more Newtonian picture of gravity is correct, well then, the stationary charge should not radiate electromagnetic radiation. But a free-falling one is accelerating and therefore it should radiate. In contrast, General Relativity sees the free-falling charge as non-accelerating. It's just going on a straight line path through curved spacetime. Whereas the stationary charge is accelerating and therefore it should give off electromagnetic radiation. Now, thus far, logistical challenges have prevented anyone from actually carrying out this experiment. But what you believe will happen reveals what you truly think about the nature of gravity. Do you think that a freely falling charge will radiate electromagnetic radiation or not? Is gravity an illusion?
This episode was sponsored by Caséta. And so I used the sponsorship money to have a rocket ship built. Caséta by Lutron makes these smart light switches. In the rocket ship, they also make remotes, motion sensors, smart plugs, basically every smart switch you could use for turning things in your home on and off. But installing a smart switch isn't rocket science. Just turn off the power to the switch, detach the existing wires, and reconnect them to the Caséta smart switch. What's great about smart switches, as opposed to smart bulbs, is one switch often controls multiple bulbs. So you can save money by replacing only the switch. And they connect to most smart devices like Alexa, Google Assistant, and Apple HomeKit. And you can control them via an app on your phone. So if you forget to turn off the lights in the rocket, no need to go back, just turn them off in the app. You can also use the app to set up schedules, turning the lights on when it goes dark. This gives you peace of mind knowing your family will always come home to a well-lit house. Now, we may not have personal rockets yet, but we have smart switches. And the smart choice for these devices is Caséta by Lutron.
