# Einstein says objects do not fall to the Earth?

1. Nov 10, 2014

### inertiaforce

According to this video, a bowling ball and a feather fall at the same rate because according to Einstein, they aren't falling:

https://testtube.com/dnews/which-falls-faster-a-feather-or-a-bowling-ball/?utm_source=FB&utm_medium=DNews&utm_campaign=DNewsSocial [Broken]

What does this mean exactly? The earth comes up to the ball and the feather?

Last edited by a moderator: May 7, 2017
2. Nov 10, 2014

### Staff: Mentor

That's pretty much right.

3. Nov 10, 2014

### inertiaforce

But isn't earth's gravity supposed to make things fall to it? And not vice versa?

4. Nov 10, 2014

### PeroK

Suppose two balls were "dropped" at the same time on opposite sides of the Earth. Which way would the Earth fall?

5. Nov 10, 2014

### Bandersnatch

Not in GR, no. That's a Newtonian conception. It's not vice versa either, as the Earth is not falling towards the objects.

In GR mass bends the "natural" path of an object through space-time. The natural path is the geodesic, objects moving on it are in free fall. It curves inwards toward mass. The surface of the Earth can't follow this natural path due to other stuff below occupying space.

6. Nov 10, 2014

### PeroK

What's the difference between "curving inward (through spacetime)" and "falling"?

7. Nov 10, 2014

### Bandersnatch

There's no force acting on an object moving along the geodesic.

8. Nov 10, 2014

### PeroK

Who said there was?

My objection to this is that GR did not change the meaning of the verb "to fall". It changed the mechanism - the explanation for the falling. But, not the experimental fact of falling. Neither the OP nor I used the word "force" at all.

9. Nov 10, 2014

### Bandersnatch

Falling requires acceleration. Acceleration requires force.

10. Nov 10, 2014

### inertiaforce

Haha. I like this. Someone please answer PeroK's question. It deserves an answer.

11. Nov 10, 2014

### inertiaforce

According to the video, the ball and the feather aren't falling though. Therefore, there is no force acting on them. The video actually said that Einstein's view was that no force was acting on the feather or on the ball.

12. Nov 10, 2014

### PeroK

Yes, that's the point. In classical, Newtonian physics, the ball falls to Earth because of a gravitational force acting on it.

But, in GR, the concept of a gravitaional force is superseded by the concept of curved spacetime. The force of gravity is no longer needed to explain why objects fall.

Beyond that it's pure semantics whether to say the ball falls or not.

For example, Newton could have done the same thing. Newton could have said: this apple is not falling, it's being pulled to Earth by the force of gravity. He provided a mechanism to explain falling, but it was not with Newtonian mechanics that objects were first observed to fall. Objects fell before Newton discovered gravity.

13. Nov 10, 2014

### Staff: Mentor

Answering this requires drawing a key distinction between local and global phenomena. Locally, you can view the ball and the feather as being at rest in an inertial frame, in which physics works exactly like it does in special relativity. The Earth is accelerating upward in this local inertial frame.

Globally, there is no single inertial frame that encompasses the entire Earth, and, as your observation makes clear, local inertial frames on opposite sides of the Earth do not "line up" with each other. This is because of spacetime curvature (which can be ignored in a single local inertial frame). So to properly account for the behavior of objects globally around the Earth, you have to talk about spacetime curvature and how it affects geodesics (the paths of freely falling objects).

However, even on this global view, it's still true that the ball and the feather would follow the same paths (the same geodesics), despite their different masses. So even globally, the motion of freely falling objects can't depend on any property of the objects; it has to depend only on properties of spacetime itself. That is the real point of Einstein's observation.

Which is correct: if you attach accelerometers to the feather and the ball, they will read zero, indicating that no force is acting on them.

This definition of "force" is different than the Newtonian one; but the Newtonian one had the disadvantage that "forces" like gravity (and also centrifugal force and other "fictitious forces") could be acting without there being any possible direct measurement of them with an accelerometer. Einstein's definition is cleaner because it makes "force" correspond exactly with direct accelerometer measurements.

I notice, btw, that you are now not using the word "falling" in connection with what the video said. Saying that no force is acting on the ball and feather is not the same as saying they are "not falling", because "no force acting" can be measured directly (as I described above), but "falling" vs. "not falling" can depend on how you choose to describe the motion, i.e., it's observer-dependent. Einstein was trying to focus on things that are not observer-dependent.

14. Nov 10, 2014

### inertiaforce

Watch from 4:02: "The reason the ball and the feather fall together is because they're not falling. They're standing still. There is no force acting on them at all. He (Einstein) reasoned that if you couldn't see the background, there would be no way of knowing the ball and the feather were being accelerated towards the earth. So, he concluded, they weren't."

15. Nov 10, 2014

### phinds

AGAIN, nothing is "falling" in GR. In the case of two balls of equal mass, each the same distance above the earth, both balls would move towards the center of gravity of the earth/ball/ball system and since that corresponds (ideally) to the center of the Earth, the Earth would not move since the center of mass of the Earth is already AT the center of mass of the Earth.

16. Nov 10, 2014

### Staff: Mentor

Can we back up for a moment?

There are two mathematical descriptions of the behavior of an object near the surface of the earth: the classical Newtonian model and the model of General relativity. Both models make the same prediction:
- To the limits of accuracy of our measurements, the speed of the object relative to the surface of the earth will be the same as the speed of the surface of the earth relative to the object, and that speed will be given by $v=gt$ where $g$ is 10 meters per second per second and $t$ is the time since the object was released.
- To the limits of the accuracy of our measurements, the distance between the object and the surface of the earth will be given by $s=H-gt^2/2$ where $H$ is the height at which the object was released.

The Newtonian model says that this is because there is a force between the earth and the object, this force is given by $F=Gm_Em/r^2$, and this force accelerates the object and the earth according to Newton's $F=ma$. The mass of the earth is so great that its acceleration is negligible so we say that the object is pulled towards the earth and not the other way around.

The relativistic model says that the earth and the object are both moving through spacetime in the nice straight lines ("geodesics" in the language of four-dimensional spacetime) that an object experiencing no force would be expected to follow. However, spacetime itself is curved by the two masses (although earth's contribution is the only one that matters here, because it is so much larger) in such a way that the two geodesics intersect and therefore the object and the surface of the earth are on a collision course. Naturally they draw closer together as they approach their collision, and the closure rate is exactly that described by the Newtonian equations.

You can use either description. The GR description is much less mathematically tractable (which is why we teach the Newtonian approach in high school, whereas GR is not even an undergraduate college subject) but works correctly in many situations where the classical description does not.

The thing you cannot do is try to carry words like "fall" or "force" or "acceleration" between the two descriptions. They have subtly different meanings in the two descriptions... Which is why in my first paragraph above, I described the common prediction made by both models without using those words.

17. Nov 10, 2014

### Staff: Mentor

Let's assume for simplicity that the two balls have the same mass.

Using Newton's model, the forces between each ball and the earth would be of equal magnitude and opposite direction, so the earth would experience no net force and the balls would be drawn towards the earth according to Newton's $F=ma$ by the forces acting on the balls.

Using Einstein's model, the geodesic paths of the two balls and the earth would intersect. The curvature of spacetime bends the paths of the two balls towards the path of the earth. Eventually they collide.

18. Nov 10, 2014

### Staff: Mentor

Hmm, I didn't watch the video, but if this is an accurate representation of what they said then I disagree with it. The term "free fall" in GR means that there is no force acting on it. So the ball and the feather are falling precisely because there is no force acting on them.

The surface of the earth is not falling because it does have a force acting on it (pressure from below).

19. Nov 11, 2014

### A.T.

I agree with DaleSpam here. The whole confusion arises from the ambiguity of the word "falling". What the OP-quote actually means by "not falling" is actually "not accelerating down in an absolute sense" (no proper acceleration). And by "standing still" they mean "being at rest in an inertial frame of reference" (there is no absolute rest).

But for pop-sci TV they have to dumb it down, and sometimes it comes out as the opposite of what an explanation in common scientific terms would be.

Last edited: Nov 11, 2014
20. Nov 11, 2014

### inertiaforce

Nugatory, I liked your explanations. Thank you.