What Teachers Get Wrong About Equivalence

Are these two situations equivalent? On the left, you're sitting on the Earth. On the right, you're inside an accelerating rocket. Either way, you feel your body pushing against the floor as if there's gravity. It's impossible for you to tell the difference. Or is it? [Intro Music] Hey Crazies. What we're talking about here is something called the “equivalence principle.” If you're accelerating uniformly, any measurements you take will be physically equivalent to measurements taken in a uniform

gravitational field of appropriate strength. It's one of the founding principles of general relativity. But is it true? And if it's not, does that make relativity invalid? We'll come back to both of these questions a little later. For now, I just want you to imagine you've woken up, locked in a room. This room has no windows. You hear no sound. You don't feel any vibrations. You're completely isolated from the world outside. This is exactly the situation I've put one of my expendable clones in.

Great. Here we go again. This is going to be hilarious. Where do you think you are, man? Well, I can't tell exactly you, but I feel my weight against the floor, so I'm going to guess this room is somewhere on Earth. Interesting. Interesting. What if I told you you weren't on Earth? Oh, so I'm on another planet with the same gravity? Nope. You're inside a rocket accelerating at exactly 9.8 meters per second squared. Weird. I can't tell the difference. That's exactly the point. The 9.8 meters per

second squared is what we call the “acceleration due to gravity,” on Earth at least. It's a gain of 9.8 meters per second for every second to travel. For some perspective, 9.8 meters per second is about 22 miles per hour or 35 kilometers per hour. Without air resistance, that's how much a falling object speeds up every second. For Expendable Clone to feel his weight against the floor, his rocket must share that acceleration. It's accelerating through deep space at the same rate that things fall

toward Earth. What most of us call “weight” is just the feeling of weight, not the weight itself. Right now, you're feeling an upward push from the ground or your chair or both. You also have a weight pulling you down, something you never feel. Sure, that upward push only exists because the Earth is already pulling you down with gravity, but what if there was another reason for that upward push? Like a rocket you happen to be inside, accelerating forward. You would feel a weight even though you

don't have one. But, just because one situation is indistinguishable from another, that doesn't necessarily make them equivalent. There may be an upward push in both situations, but only one has a weight. Right? We're not saying his contact with the floor is gravity, are we? The equivalence principle seems to say so, but that's kind of sus. And a huge part of science is tearing ideas to shreds for the benefit of all humankind. Whatever survives is the truth, or at least approximately the truth.

So let's see if we can find an exception to this rule. What if we bring in another object, say, a squirrel? From the comfort of our space station, we see a squirrel floating stationary in space. As the rocket accelerates upward, the squirrel slips through a hole and into the rocket. From Expendable Clone’s point of view, it would be as if a squirrel fell from the sky into his room. It's a perfectly reasonable conclusion. Not only does the squirrel fall, but it falls in exactly the same way that

it would if it were falling on Earth. It's as if there's a gravity acting on the squirrel, even though we know there's no source of gravity nearby. The equivalence principle still seems to hold up. Hmm. What if we have the squirrel come in from the side instead? Let's say the squirrel is moving in a straight line sideways. As the rocket accelerates upward, the squirrel slips through a hole in the side of the rocket. Expendable clone will see the squirrel enter his room from the wall and then fal

l to the floor in an arc as if there was gravity. If we could see inside his room, we'd see the squirrel still moving in a straight line. It would be the floor accelerating upward. But, according to my clone, it's the squirrel that accelerates downward like a projectile. To him, it looks like there's gravity. The equivalence principle still holds. I think it's time for something a little more extreme. Let's say his rocket is like, 20 miles long, and he's running up the stairs. Every ten floors o

r so, he stops to measure his weight with a bathroom scale. No matter what floor he's on, his weight will always be the same. That wouldn't be true with a 20 mile tall building. In that case, your weight would gradually decrease as you went up floors. Your weight on the top floor would be 1% less than your weight on the bottom floor. Bingo Bango! Equivalence Principle broken. (Off Camera Voice) Wait a minute. That's not a uniform gravitational field. Oh, crap. This principle does require that gr

avity be uniform. And that's only approximately true near the surface of the earth. If you get far enough away, we stop being able to make that approximation. Not only does gravity get weaker with distance, it can also turn. Down is toward the center of the earth, which isn't always the same direction. Earth is round and sometimes we have to account for that. Really long bridges are a good example. If we were to drop two squirrels a mile apart and from a mile high, they'd be 1.3 feet or 40 centi

meters closer together by the time they hit the ground, which is yet another situation where the equivalence principle does not apply. If the accelerating rocket was a one mile cube, the two squirrels would stay exactly one mile apart the entire fall. The equivalence principle only compares uniform acceleration with uniform gravitational fields, but it was never meant to be a universal law. Its purpose is to help us design thought experiments, so we can ask the right questions. The experiments i

n this video seem to suggest that gravity is simply acceleration we can't see. Since they only happen in our minds, they can't tell us if that conclusion is true. But if it is true, it can tell us what consequences we might see. Remember when we had a squirrel enter Expendable Clone’s room through a wall? Well, what would happen if a pulse of light entered the room instead? It would also bend toward the floor like the squirrels path did, just not nearly as much. The bend would be subtle because

light is fast. Fast Fast! If we believe the equivalence principle, and we haven't found any reason not to, then that means light should be affected by gravity, just like squirrels. Which seems absolutely bonkers. There's a reason people didn't believe Einstein and Hilbert when they published this in 1915. They had to actually prove it, which means they had to wait for a total solar eclipse and for a World War 1 to end. Europe was leading science at the time, and they were understandably kind of

a mess. Anyway, the idea is that if light from a star passes close enough to the Sun on its way to Earth, then the Sun will bend its path, making it appear in a slightly different location in the sky. And I mean slightly. They estimated the deflection angle to be less than two arcseconds. That's less than an 1800th of a degree. The U.S. tried to do the experiment in June of 1918 in Baker City, Oregon. That was near the end of the war. But, alas, it was cloudy with a 100% chance of failure. The n

ext total solar eclipse wouldn't happen until May of 1919. European scientists planned out two expeditions: one for several Brazil in South America and the other for Príncipe in Africa. The hope was that at least one of them would get decent images. And, after some technical difficulties, both teams managed it. Here's one of the images from Brazil. The results of this experiment confirmed that prediction from general relativity. Light is, in fact, affected by gravity, just like squirrels. As far

as we can tell, gravity is just acceleration we can't see. The equivalence principle might not apply to solar eclipses. But it did present us with a thought experiment, which led us to conduct a real one. A real experiment we never would have thought to do otherwise. So is the equivalence principle true? Yes. Is it universal? No. But that doesn't mean it hasn't been extremely useful. And until next time, remember, it's okay to be a little crazy. Let's talk about Nebula, a different kind of stre

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