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You are now accelerating: What it means that gravity is not a force
🕑 Added 2023-12-23 13:00:07 +0000 UTC[This is a transcript.]
This video is all about Albert Einstein, yes, that guy again. Einstein is famous for his theory of general relativity. Itâs taught us that gravity is not a force. And thatâs probably the most misunderstood physics fact, ever. Like, even physicists get it wrong, all the time. Gravity is not a force. And since thereâs no force pushing down on you, that means you are currently accelerating upward. Unless youâre watching this from the ISS, in which case please say hi to the moon.
How does gravity work if itâs not a force? Thatâs what weâll talk about today.
An accelerometer is a device that measures acceleration. If youâd hold an accelerometer steadily in your hand, itâd tell you itâs accelerated upwards. This isnât 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 itâs lying still on a table. It tells you itâs accelerated upwards.
And this is entirely correct. If you hold an accelerometer still on the surface on earth, itâs 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. Itâs like when youâre trying to accelerate a car with your hand. Itâll push against it.
If you hold something in your hand, thatâs not the gravitational force pushing it down. Because gravity isnât a force. Itâs pushing on your hand because you are accelerating it upward.
Why is the thing in your hand accelerated if you donât move your hand? Itâs because *you are accelerated. And *you are accelerated because thereâs a force pushing on you from below. Thatâs the floor, or rather the atomic bonds in the floor and in the ground below.
You see, the entire earth has internal pressure, otherwise itâd 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, thereâs also the gravitational force pushing down, so the two forces balance to zero, right? Noâoo. Because gravity is not a force.
Gravity is a consequence of moving in a space-time thatâs been curved by the presence of masses. If there are no masses nearby to curve space-time, itâs flat. So long as thereâs 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 âattractedâ to the bigger one. Itâs a pretty good visualization, itâs just that you shouldnât ask why the big marble bends the rubber, then it gets really confusing.
So in this curved space around a planet, if thereâs no force acting on you, you fall towards the planet. Thatâs not an acceleration. But if something gets in your way, like the surface of the planet, then *that creates a force. So now youâre accelerated.
This is why thereâs no force pushing down on you right now. Thereâs only a force pushing up. If you took away the surface of earth, youâd fall. And if you fell, thereâd be again no force acting on you.
This is also why the earth would collapse if it had no internal pressure. Itâs not because thereâs a gravitational force acting on the matter. Because gravity isnât a force. Itâs 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 letâs 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 donât know, maybe Bob the astronaut lost it on a spacewalk? I hear these things happen.
Ok, thereâs a spring in outer space for whatever reason. Itâll have some extension. Now if you tie that spring to a rocket and that rocket blasts off, whatâs going to happen with the spring? Itâll 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 isnât 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. Itâs 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 Einsteinâs theories have the word ârelativeâ in them.
This brings us to the third, and most important point that we learn from the spring. Acceleration is not relative, itâs absolute. You can measure how much youâre 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. Whatâs this got to do with gravity. Well this is where Einsteinâs genius comes in. Einstein said, letâs put the spring in a box from which you canât look out. You have no idea whatâs 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 youâre in the box, you canât tell whether youâre being accelerated, or whether you are sitting still on the surface of a planet. He then said if there isnât any measurement that you can do to tell these situations apart, theyâre 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 whatâs called the âEquivalence Principleâ.
The point where people usually go wrong is to conclude that because gravity is indistinguishable from acceleration, that means gravity accelerates you. But that isnât so. Because to accelerate something, you need a force. And gravity is not a force. Einsteinâs 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 canât 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 donât 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 Einsteinâs general relativity to calculate what happens. Theyâll tell you that if you get too close to the horizon, youâll inevitably cross it and then youâll end up in the singularity. Which might not be there, but thatâs a different story. The point for today is that your spring wonât budge because thereâs no force acting on you. Because gravity is not a force.
This is what physicists mean by âfree fallâ in a gravitational field. It means thereâs no force acting on you, so youâre not accelerated. A zero-g flight is the closest youâll get to that on earth â at least if you want to survive.
The idea of a zero-g flight is exactly einsteinâs elevator experiment. That if youâre in a box whose floor is not pushing on you, thatâs the plane, you canât tell whether youâre in outer space far away from any heavy objects, where space-time is flat, or whether youâre freely falling in a curved space-time. Physically, itâs exactly the same. So the zero-g flight is indeed a good simulation for outer space. And why is that? Itâs because gravity is not a force. In the plane, you are falling in a gravitational field, but thereâs no force acting on you.
Now, I sometimes hear people say that âzero-gâ is a bad term because it suggests that thereâs no gravity, but of course the curvature of space-time doesnât go away just because you sit in a plane.
And thatâs right, but zero-g doesnât mean zero-gravity. The âgâ is the local acceleration that you experience if you are in rest in the gravitational field. If you are on the earthâs 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 isnât 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 earthâs mantle, but I digress.
To come back to zero-g flights. On a zero-g flight your acceleration is indeed almost zero because youâre not at rest with the surface of earth, thatâs why it feels like free fall. Of course itâs not exactly zero, because you always move around somewhat that way or this way, or if youâre Rohin you are doing CPR, but itâs pretty close to zero. So Iâd say, zero-g is a good description. Same thing on the ISS.
Okay, but I can see that youâre still confused because you learned that acceleration is a change in velocity. And if youâre not changing velocity, youâre just standing on earth, how can you be accelerated?
Well, the entire point of einsteinâs theory of relativity is that velocity is not an absolute. What you mean if you say youâre not changing velocity is that youâre not moving relative to the surface of earth. But this doesnât mean you have zero velocity, because thatâs a meaningless statement. It just means you are not moving relative to something else thatâs 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 âno accelerationâ. 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 thereâs 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 youâre on top of the building that force of gravity cancels that from the building pushing on you. So now thereâs no net force acting on you and Newton says youâre not accelerated. If you jump off the building, Newton would say, the force from below disappears and thereâs only the gravitational force acting on you and youâre accelerated. And if you hit the ground, you suddenly return to zero acceleration.
The Newtonian picture is the one we learn at school, and itâs useful so long as you are on earth. But strictly speaking itâs wrong because you canât just redefine what you mean by zero acceleration. You canât do that because acceleration itâs not a relativity quantity. If youâre 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 theyâll sometimes refer to gravity as a force even though it isnât. A typical example is when they speak of the âfour fundamental forces of natureâ. If theyâre being careful though, theyâll refer to it as the âgravitational interactionâ and the âfour fundamental interactionsâ. But often they donât. I think they really just call it a force because that starts with an âFâ.
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.
Comments
The first time that I heard of mountain ranges have lower gravity surprised me because I thought that there would be more matter in mountains and thus higher gravity; Continents are less dense than the mantel but there is more less dense material in mountain ranges than in the middle of continents, so I thought that mountain ranges would have greater gravity. Oh well, mysteries.
Accelerometer Experiments Prove and Clarify Einsteinâs Gravity Theory A single poster and a short article capture how spacetime curvature results in gravity: https://davidlevitt.medium.com/accelerometer-experiments-clarify-einsteins-gravity-theory-9b57e50499e3 Along with Fictitious Force, Proper Acceleration, Proper Force and Weight, it very concisely covers things like: * how modern students can clarify and prove Einsteinâs gravity theory with an iPhoneâs accelerometers * how spacetime curvature answers âHow can the earthâs surface accelerate outward at 1 g without the planet getting any bigger??â, letting us finally understand why gravity requires non-Euclidean geometry * how both meters and seconds vary in length in the vicinity of matter * how a volume of space can have an acceleration without having a velocity in any direction * what Profs Feynman and Kip Thorne thought about fictitious force in general relativity * how Newtonâs G and volume acceleration elegantly capture Einsteinâs and Thorneâs space âwarpageâ * how this approach makes it simple to derive Newtonâs, Gaussâs and Keplerâs laws as results of curvature * how thatâs also expressed simply and quantitatively in Einsteinâs field equation * why Newton and Einstein were both dissatisfied with their own theories and their presentation * The key reasons why so many physicists have problems accepting and explaining this. In fact itâs a quick read and very easy to understand, with much less math than most general relativity curricula, and is thus effective for a broad audience. Sabine, since like me youâre writing and teaching in this area, Iâm very interested in your take on the article. I would likewise love to chat with commenters here seeing this video and seeking to understand the material better.
Every profession, from medicine to brick-laying, has its own "terms or art", or "jargon." This is a code, accepted and understood by everyone in the same profession, that makes communication easier for those in this profession ("pass me the Bahco" is more effective than "pass me the thingy" and even than "pass me the cabinet scraper", as there may be different kinds in the furniture-making shop). It is not meant to demean, or insult, or despise, or keep out those not in it. Or declare to the World that some words are exclusively for their use in a certain profession and nobody can use them differently than how those professionals do it. The mathematics and the physics trades are not different than any other in this respect. If this makes it difficult to follow "for most people", that is not surprising, because it is intended to be understood and used by those who are in the profession, who are not "most people." Fact of life. You might just as well complain that the sky can be, and often is, blue.
Continuing: Curved spacetime is a brilliant model. I gather you can get the same answers with flat spacetime and the right gauge fields: https://arxiv.org/abs/gr-qc/0405033.
Physics and Mathematics take words with a normal human meaning and give them a technical meaning, then claim that the technical meaning is "right" and the ordinary meaning is wrong. Where I am the Sun has just risen, and all the furniture in my room is at rest. If you want to look at this with a different perspective while using words which have a different meaning in ordinary language, then it is a problem for most people.
