From: veritasium
In general relativity, gravity is presented not as a force or gravitational field, but as an illusion [00:00:17], [00:00:22], [00:05:28]. This perspective fundamentally redefines the concept of acceleration and what constitutes an inertial observer.
Defining an Inertial Observer
According to Albert Einstein, an inertial observer is akin to someone who is weightless [00:01:03]. This idea originated from his “happiest thought”: imagining a man falling off a roof [00:00:50]. While falling, the man would feel weightless [00:01:08], and any objects he dropped would remain stationary relative to him or move in uniform motion [00:01:12]. This scenario is equivalent to being in deep space, away from large masses, with a spaceship at rest or coasting at a constant velocity [00:01:23], [00:01:28]. In such a state, one feels no weight [00:01:34], and objects remain stationary or move in straight lines at constant velocity after a push [00:01:37]>.
An inertial observer is characterized by:
- Not accelerating [00:01:50].
- Not being in a gravitational field [00:01:50].
- All laws of physics applying in their reference frame [00:01:54], meaning no experiment can distinguish their inertial reference frame from any other [00:01:57].
Einstein’s Equivalence Principle
The Equivalence Principle states that the sensation of weightlessness (like the man falling from a roof or the “Rocket Man” in deep space) means one is in an inertial frame of reference [00:02:09], [00:03:01]. This implies that the man falling from the roof is not in a gravitational field and is not accelerating; he is an inertial observer [00:02:17], [00:02:21].
This perspective is counter-intuitive in Newtonian physics, where the falling man is clearly accelerating due to Earth’s gravity [00:02:35], [00:02:41]. However, Einstein’s Equivalence Principle shifts the focus to the observer’s experience [00:02:55]. If an observer feels weightless, they are in an inertial frame [00:03:01]. For example, Rocket Man, even when his path appears curved to an external observer as he approaches a planet, remains oblivious inside his rocket, feeling no force or acceleration [00:03:30]>, [00:03:34]>. An onboard accelerometer would register no change [00:03:50]>. He continues on his inertial path through spacetime until he crashes into the planet [00:03:54]>, [00:03:59]>.
Curved Spacetime and Geodesics
The appearance of a curved path for an inertial observer (like Rocket Man) is explained by curved spacetime [00:04:18]>. An inertial observer always moves in a straight line through spacetime [00:04:21]>, [00:04:29]>. However, spacetime around massive objects like planets is curved [00:04:32]>, making the straight line path appear curved to a distant observer [00:04:36]>.
These “straightest paths” over curved surfaces are called geodesics [00:04:55]>. Inertial observers follow these geodesics through curved spacetime [00:04:59]>, [00:05:02]>. An analogy is two people walking due North from the equator: they appear to be pushed together, but they are simply following straight paths (geodesics) on a curved surface (Earth) [00:05:08]>, [00:05:33]>.
Astronauts on the space station are weightless, meaning they are inertial observers traveling on a geodesic [00:05:42]>, [00:05:46]>. The Earth curves spacetime around it, which is why their straight line path appears as a helix, only looking like a circular orbit if the time dimension is ignored [00:05:50]>, [00:05:58]>.
“Matter tells spacetime how to curve, and spacetime tells matter how to move.” [00:06:48]
Acceleration in General Relativity
In general relativity, the perception of “being at rest” on Earth’s surface is equivalent to accelerating in a rocket ship in deep space [00:07:36]>, [00:08:01]>. If you feel weight (i.e., not weightless), you are not an inertial observer [00:07:54]>, [00:07:57]>.
While Newtonian physics describes the normal force from the floor balancing the gravitational force, implying no acceleration [00:08:34]>, [00:08:45]>, general relativity states that there is no gravitational force [00:08:50]>, [00:08:55]>. You have no weight [00:08:57]>. Therefore, the only force acting on you is the normal force pushing you up, meaning you are accelerating upwards [00:08:57]>, [00:09:01]>.
In curved spacetime, you need to accelerate just to stand still. [00:11:02]
This acceleration is a deviation from a geodesic [00:09:37]>. The floor prevents you from following a straight line path through spacetime, applying an upward force that causes you to accelerate upwards [00:09:46]>, [00:09:52]>. This is possible even if your spatial coordinates are not changing, due to the curvature of spacetime and your velocity through time [00:10:06]>, [00:10:13]>.
Why All Objects Fall at the Same Rate
A classical mystery in Newtonian physics is why all objects fall at the same rate. The explanation relied on the seemingly coincidental numerical identity of gravitational mass (which experiences a gravitational field) and inertial mass (resistance to acceleration) [00:11:13]>, [00:11:45]>, [00:11:49]>.
In general relativity, there is no mystery [00:12:20]>. All objects appear to fall the same way because they are not accelerating [00:12:23]>. They are simply following straight line paths (geodesics) through spacetime until something stops them [00:12:28]>. Similarly, objects in a rocket ship appear to accelerate at the same rate because they are not accelerating; it’s the floor of the rocket accelerating into them [00:13:33]>, [00:13:37]>.
Experimental Validation and Predictions
The concepts of inertial observers and general theory of relativity and gravity were validated through key astronomical observations supporting general relativity.
Bending of Light
Einstein predicted that if an accelerating frame of reference bends light, then light must also bend when it passes a large mass [00:13:12]>, [00:13:40]>, [00:13:58]>. This was famously tested during a total solar eclipse in 1919 by Arthur Eddington [00:14:27]>, [00:14:33]>. His observations of stars near the sun showed their positions were deflected by the precise amount predicted by Einstein’s general theory of relativity [00:14:40]>, [00:14:43]>, a result twice the deflection calculated by some using a strictly Newtonian model [00:14:51]>.
Accelerating Charges
A proposed experiment to further test the nature of gravity involves comparing the behavior of a stationary charge in a gravitational field to a free-falling one [00:15:17]>, [00:15:20]>.
- Newtonian Picture: A stationary charge should not radiate electromagnetic radiation, while a free-falling one (accelerating) should radiate [00:15:27]>, [00:15:30]>.
- General Relativity Picture: A free-falling charge is non-accelerating (following a geodesic), so it should not radiate. A stationary charge is accelerating (deviating from a geodesic), so it should give off electromagnetic radiation [00:15:39]>, [00:15:44]>, [00:15:48]>.
Logistical challenges have prevented this experiment from being carried out, but the predicted outcome reveals one’s underlying belief about the nature of gravity [00:15:55]>, [00:16:00]>.