In a PBS Space Time video the narrator states that, in Einstein’s opinion, an object perceived to fall to the ground should actually be viewed as the earth rising up to meet the object. I couldn’t quite follow the concept. I understand that gravity bends space, which is basically a restructuring of the dimensions around a massive object. But I still can’t make the connection. Can someone here explain it better?
Without having seen the episode it is difficult to say exactly what they mean, but an object also exerts an equal and opposite gravitational force on the Earth and so the Earth will be attracted to the object. For objects with much smaller masses than the mass of the Earth this force is negligible.
The two-body problem in general relativity cannot be solved analytically, but you would expect to see time-dependency in the spacetime metric manifested as gravitational radiation in the far-field.
I wonder if the point is a more trivial one, that the earth is just a body like any other, and behaves according to the same laws as a basketball or a fish-cake. I.e. it’s wrong to imagine that the earth is stationary and acting in a special way.
There is no preferred reference frame.
From one perspective it looks like the object falls to the earth. From another it looks like the earth falls to the object.
Think of it this way:
You are alone in a completely empty universe (as far as you can tell). You see absolutely nothing. You are just floating there in the empty vacuum of space.
Then you notice, in the distance, something approaching. In time it grows larger and larger. To your amazement you see a planet approach and then pass by you and eventually recede into the distance and disappear from sight.
Who was moving?
From your perspective you were just sitting there and a planet flew past. From the planet’s point of view it was you who was moving.
There is no way for you to say with certainty whether it was you or the planet or some combination of movement that can tell you what really happened. All solutions that describe that motion are equally valid.
I found the video: Is Gravity An Illusion? - YouTube
Unless you are a whale or a potted petunia. Then you hit it.
On no, not again.
So the sun does revolve around the earth…
Both the object and the earth exert gravitational force upon each other. So the object pulls the earth toward it, and the earth pulls the object to the earth. So you could say they meet somewhere in between them.
Of course, the force of gravity from each is proportional to their mass. Thus the gravity from a 1 kg object compared to that from a 5.9x10^24 kg earth is vanishingly small, negligible. Probably less effect than the sunlight hitting the earth on the daylight side. And there’s probably some person on the other side of the earth dropping a similar object, and canceling out the effect.
So in practical, real-world terms, you can ignore the object’s gravity, and say it ‘falls to the earth’. Just like in most things we humans do, you can ignore Einstein’s relativity – Newton’s Laws are accurate enough for human-scale activities. But to a physicist, talking about the actual forces, it isn’t completely accurate to say ‘falls to the earth’.
Consider an example that is closer to our model of perception, the Great Circle routes on Earth.
While we perceive the ground as flat that is purely an artifact of our frame of reference. In that image the red line is the path that we would take if we went straight but the red line is the shortest path, or the geodesic which can be thought of as the shortest distance between to points.
While part of this effect is due to how maps are projected, it is also intuitive if you try it on a globe. Grab a piece of string if you have a globe and and guess that the straight path is from San Francisco and London, then pull that piece of string between those two points on the globe and it will most likely be another path.
Now take the time watch this video from 17:00 to ~ 19:00. related to what can be viewed as a curved path can actually be a straight path.
In space time we have four dimension, one of which is temporal which is time. While we have no ability to control our travel through that dimension it is one that we are moving in all the time. Given the chance we would follow the straightest path possible through it.
We have a maximum rate that we travel through time, and more than that it is the same for everyone from all reference frames. If we diverge from that path through acceleration or movement through the spacial dimensions we actually lengthen our path and that divergence actually results in us experiencing time slower because our path is longer and we are no longer following the geodesic in that path.
Notice how difficult it is for us to really conceptualize this in our minds.
Now consider that really that the Great Circle Route is not actually the shortest route, because if it wasn’t for the ground we could slice into the globe and find a shorter path. When we sail, walk or drive we don’t feel like we are climbing a hill when following that route, but we are traveling in a arc if you bisected the globe along that path.
It takes a lot of work to try and understand why it is probably more correct to view the earth rising up to meet the object, but one way to conceptualize it is to consider the above, while realizing what you experience as weight is actually the earth consistently accelerating you away from your preferred, shortest path or geodesic through spacetime.
To be fair, while this subject is hard to understand it is made more challenging that people prefer to use the simplest math possible to solve problems. While the GR model is far more accurate the Newtonian model is pretty damn close and good enough for most of our needs. So everyone tends to use the Newtonian model if at all possible. Gravity is a fictional force under GR, which is just a perceived force from a specific frame of reference that is really caused by the curvature of spacetime.
A falling apple or a tossed baseball are actually going through a straighter path through time, but the pesky earth keeps running into them and pushing them away on a longer path.
Or a jackknifed juggernaut in free fall.
That is true if there is no acceleration, but in the OP’s case the apple is accelerating towards the earth and so is not in an inertial frame.
I think the point probably was that gravity is (locally) the same as acceleration, as with the more famous elevator example: you can’t tell the difference between the ground accelerating ‘up’ and the ball falling ‘down’. Thus, the force of gravity and the pseudoforce experienced in an accelerated frame of reference are indistinguishable, which is a formulation of the equivalence principle.
Ever since the big bang, everything in the universe has been in motion. That is, still moving away from the bang’s location, wherever that was. Many things aren’t moving in completely straight lines. We were always taught our moon orbits the Earth, which orbits our local sun, which is slowly orbiting something at the middle of our galaxy. All that is true, but all those objects are still moving away from “bang zero.” That means our yearly orbit around the sun is really sort of a spiral through the overall space. The actual shape and speed of that spiral is something I can’t tell you. That would exceed my understanding, if I haven’t already crossed that boundary.
We know exactly where the location of the Big Bang was: it was right here. Oh, and over there. In fact, it was everywhere: the Big Bang wasn’t some explosion happening in space, it was space itself starting to expand; so something moving away from the location of the Big Bang doesn’t make any sense—there’s no ‘where’ there it could move to.
Thanks for this very nice summary. It brings together a few of the concepts in that video. Also, that Frames of Reference video should be a must-watch in high school physics classes.
Or, to put it another way: an apple freely falling towards the earth is in an inertial frame. It’s the apple sitting on the ground that isn’t.
The fun part if you ignore the math is just how crazy these geodesics get in the presence of spinning and charged bodies. Even in GR people tend to model schwarzschild (non-spinning, non-charged) or kerr (spinning, non-charged) black holes because the math becomes insane.
But with the Gaia data release 2 there have been some interesting bits of information coming out.
While the paths may be hard to track as there are 75 globular clusters in the halo of the Milky Way and 12 dwarf galaxies in this video. Every one of these paths is, for the most part a “straight line”
It is important to remember that ignoring tidal forces that orbits are not “Accelerated” in GR.
I expect, looking at the rotation of the large magellanic cloud that there will be some adjustments, findings and clarification on dark energy soon.
While these discovery’s may not come from me, I had to invest in an updated system to even poke around in this data. While still on a timescale that is too short to explain everything, I expect that we will have a few of the wags related to the galaxy rotation problem ruled out over the next few years.
But I mostly wanted to clarify something up thread. When simplified down to two systems; the Sun does not orbit the Earth, nor does the Earth orbit the sun, they both co-orbit a shared barycenter and are orbiting each other.
This is a minor point that isn’t important until you want to dig in deeper. Consider the case of Pluto if the tiny effect of the Earth/Sun system is a challenge.
If Jupiter was as close to the sun as Mercury even the Eris’s sun would be inside the sun at the closest approach. The fact that we can use the assumption that the Earth is orbiting the Sun for most of needs is just a special case (and a very fortunate one for us at that, both for the simple math and the not burning up part.)
The point being, remember in the back of your mind that it is the Sun/Earth system, and it is the Earth/Apple system. It is completely valid to choose either the apple or the earth’s perspective for your reference frame at our scale assuming that is the way it works will cause issues outside of our special case. Just be happy that the math is simpler by picking the Earth’s frame of reference.
Choose the reference frame that makes your life easiest without forgetting that you are picking a reference frame to make it easier.
An important point: We think of things as going down when dropped, and hence the corresponding movement of the Earth would be moving up. But this is not correct, on either point. A dropped object can be moving in any direction initially. When you throw a ball as hard as you can straight up, the ball starts falling immediately, as soon as it leaves your hand. It’s moving up while falling, but that’s not a problem. And the Earth, at least in any reference frame convenient for daily life, is not moving at all.
What a falling object does is it accelerates downward. Or, from the Einsteinian point of view, the surface of the Earth accelerates upwards. It’s when you try to explain how the Earth can be accelerating upwards both here and in Australia, while staying a constant diameter, that you start getting into all the math about curved spacetime.