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I think that the answer is no, but in some sense it feels counter intuitive so I just wanted to check here.

So if I understand it correctly, the General theory of relativity tells us that any sufficiently small object in orbit around Earth (that does not "experience" any forces) essentially follows a straight line through the curved space time, that its experience would be essentially indistinguishable from traveling through deep space in a straight line. Is that the case?

If so, this feels a bit freaky, since from our point of view here on Earth we can clearly see that objects in orbit are turning, yet they experience no lateral force.

Addy
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    Re, "no centrifugal force." Centrifugal force from what? Do you mean, the "force" due to the orbit itself? In the Newtonian model, that force is exactly equal and opposite to the force of gravity, that otherwise would cause the spacecraft and passengers to fall to the ground. – Solomon Slow Oct 12 '20 at 13:34
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    I recommend changing ".. any object in orbit..." to "... any sufficiently small object ...". A large enough object will 'feel' the stretching and squeezing due to the inhomogeneous field around a central body. – Alfred Centauri Oct 12 '20 at 13:35
  • My previous mental model (of a stable orbit) was that the object in the orbit has some velocity in the direction of the tangent of the orbit and the gravity is what curves the path. Essentially a rotating ball on a tether. In this model the object experiences centrifugal force (I believe equal and opposite to gravity). But clearly, this model is wrong and that's not what happens in reality. – Addy Oct 12 '20 at 15:02
  • New Veritasium video: Why Gravity is NOT a Force – mmesser314 Oct 18 '20 at 02:26

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You are essentially right. In free fall, you are in an inertial frame of reference, there are no forces acting on you. You follow a "straight" path through space-time, though it might be better to say "least curved" path. You can read more about "straight" paths in curved space-time in my answer to If gravity is curvature of space why are more massive objects “heavier?”.

When you stand on the ground, you are accelerated away from this path by the force of the ground pushing up on you.

We often treat the surface of the Earth as an unaccelerated inertial frame of reference, particularly when thinking of horizontal directions. We want $F = ma$ to work. But there is the force from the ground pushing upward, and $a= 0$. So we add a downward force that acts on everything to the left side of the equation. This is the force of gravity. The force of gravity is a pseudo-force.

There are other pseudo forces, such as centrifugal force and Coriolis force. You can read about them in Pseudo Force and Inertial and Non-Inertial frames and Coriolis Force: Direction Perpendicular to Rotation Axis Visualization.

Gravity is a counter-intuitive one because it isn't obvious that free fall is an inertial frame of reference. After all, it is obviously accelerating toward Earth.

mmesser314
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  • Your linked answer is very interesting, I am curious about the origin of the force from the ground pushing upward. You say that objects in spacetime follow the geodesic, also that essentially everything in our universe is traveling by the speed 1 second/s into the future which is sort of equivalent to 1 light-second of distance in the spatial dimensions. Is this "constant" time velocity the reason why we have to be accelerated upwards to stay at rest on Earth? That we always have this velocity in the time direction and the geodesic of the spacetime simply leads to the center of Earth? – Addy Oct 12 '20 at 15:32
  • I have one more interesting question, isn't the reason why curvature of spacetime seems so intangible to us pretty much the fact that we observe world mainly by detecting photons and given their speed, their geodesics around the Earth are essentially flat, while the geodesics of objects that travel at everyday speeds are significantly more curved? Maybe if the light followed the same path as everyday objects, this would be more obvious to us? This is of course a pure speculation question, just checking my intuition. – Addy Oct 12 '20 at 15:42
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    Following a geodesics would lead underground. The ground is rigid and prevents us from falling through the ground. So the origin of the upward force is the molecular bonds that make the ground rigid. But what I think you really want to know is why a following a geodesic accelerates us toward Earth. I have no quick answer to that. – mmesser314 Oct 12 '20 at 16:36
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    The spatial parts of the trajectory of a bullet or a rock are curved enough to notice. But if you add in the time part, the other end of the trajectory that lasts 1 sec is the equivalent of 186000 miles away in the time dimension. A trajectory that long that only bends a few feet is very flat. The trajectory of a rock, bullet, and photon have the same curvature. – mmesser314 Oct 12 '20 at 16:39
  • I was wondering whether any object in spacetime could be at rest, but it seems that the velocity through time is given. That's what I was aiming at with the first question. But the notion of the molecular force is actually very useful. Still though, if I place an object at rest (with 0 spatial velocity) into flat spacetime, and then another object into earth's orbit with 0 spatial velocity relative to Earth, where does the acceleration of the second object come from? It seems that work is being done in the second case, is that just an illusion? What's the difference between the 2 situations? – Addy Oct 12 '20 at 20:01
  • I see, so the difference really is the time length of the trajectory, the trajectory of light lasts only a fraction of a second, that's why it appears "straight". Furthermore, what we observe as humans in the spatial dimension as a trajectory of the rock could be thought of as a projection to the spatial dimensions, right? The time dimension seems very compressed in our experience (distance of 1 second feels much less than 300000 km) so even though it traveled a light second in the time dimension, we notice mainly the part projected into the space dimensions. – Addy Oct 12 '20 at 20:11
  • I am confused now. Isn't somehow related to the reference chosen? Like on a carousel? – Alchimista Oct 13 '20 at 12:59