General relativity free fall why

I'd suggest asking: "How do we determine whether some given constituent of Earth's surface, such as a cliff, is held from dropping ; or to which extent it is not? Einstein Field equations, Maxwell equations etc. But my mind is concerned with the physical reality of it. What causes these phenomenon to happen that can be understood and accepted by our brains. This is where the "Why" comes in. The ostensible equations are thus induced as theorems of the respective theory. Add a comment.

Active Oldest Votes. Improve this answer. Consider this: two bodies are in free fall diametrically opposite to earth's COG. Now if the earth is acc. By this argument if observers were in free fall along the Earth's perimeter, would Earth be inflating like a balloon in trying to acc.

Even the above situation can be explained by geodesics. In fact the falling observer does indeed track a geodesic in your frame of reference. But, in the terms of your question, with just one observer, it is easier to be accounted by the Equivalence Principle in itself. But two more questions come up to me: Q1 Suppose a body is slowly descending in a downward firing rocket in a tunnel dug through Earth's surface and switches off the rocket just as it reaches earth's COG.

My brain says that it would remain suspended there with the COG and body locally becoming inertial I'm assuming the body is point mass else the tidal force would rip it apart.

Is this what actually would happen? Einstein proposed the equivalence principle as the foundation of the theory of general relativity. According to this principle, there is no way that anyone or any experiment in a sealed environment can distinguish between free fall and the absence of gravity.

Different locations in a real laboratory that is falling freely due to gravity cannot all be at identical distances from the object s responsible for producing the gravitational force. In this case, objects in different locations will experience slightly different accelerations. But this point does not invalidate the principle of equivalence that Einstein derived from this line of thinking. Wolff National Optical Astronomy Observatory with many contributing authors.

The Principle of Equivalence The fundamental insight that led to the formulation of the general theory of relativity starts with a very simple thought: if you were able to jump off a high building and fall freely, you would not feel your own weight. In an elevator at rest, you feel your normal weight. In an elevator that accelerates as it descends, you would feel lighter than normal. In an elevator that accelerates as it ascends, you would feel heavier than normal.

If an evil villain cut the elevator cable, you would feel weightless as you fell to your doom. Gravity or Acceleration? Two people play catch as they descend into a bottomless abyss. Since the people and ball all fall at the same speed, it appears to them that they can play catch by throwing the ball in a straight line between them. Within their frame of reference, there appears to be no gravity.

Shane Kimbrough and Sandra Magnus are shown aboard the Endeavour in with various fruit floating freely. Because the shuttle is in free fall as it orbits Earth, everything—including astronauts—stays put or moves uniformly relative to the walls of the spacecraft. This free-falling state produces a lack of apparent gravity inside the spacecraft.

The Paths of Light and Matter Einstein postulated that the equivalence principle is a fundamental fact of nature, and that there is no experiment inside any spacecraft by which an astronaut can ever distinguish between being weightless in remote space and being in free fall near a planet like Earth.

In a spaceship moving to the left in this figure in its orbit about a planet, light is beamed from the rear, A, toward the front, B. Meanwhile, the ship is falling out of its straight path exaggerated here. Can we find similar effects in spacetime? Then we would have found curvature. So what we seek is a sheet of spacetime in which we find converging or diverging curves.

As we shall see, that will be easy to find. A collection of masses in free fall in a gravitational field will provide exactly the sort of curves we need. To get us started, we will take the simplest case as far as the curvature is concerned, although the set up physically is a bit messier. Imagine, for example, that it is released from rest halfway between the surface and center. It would take the same 42 minutes to cross the center and come momentarily to rest at the corresponding point on the other side of the center; and then another 42 minutes to make the trip back to its starting point.

If you compare this spacetime diagram to the earlier figure of the travelers on the earth's surface, you will see that they agree in the essential aspect. They both show converging trajectories, the hallmark of positive curvature. This allows us to interpret the gravitational motions in a novel way.

The temptation is to call this convergence "geodesic deviation. They are not in Newtonian theory. In relativity, both special and general, they are timelike geodesics. That is, they are curves of greatest proper time, which is the analog of the straight lines of Euclidean geometry, the curves of shortest distance.

So we can yield to the temptation and, in so doing, arrive at the essential idea of Einstein's theory. This case of free fall inside the earth turns out to be an especially simple case as far as curvature is concerned in two ways. Second, the magnitude of the curvature does not depend on the mass or size of the earth; it depends only on the mass density of the earth. This is not obvious. An easy calculation in Newtonian theory can show it, however.

These last two points are important enough to be stated in a relation that is close to but not quite one that holds very generally:. In this formula Newtonian "mass density" has been replaced by the vaguer "matter density" in anticipation of what will transpire in general relativity, where the density of matter is a more complicated quantity that embraces energy and momentum densities as well as stresses.

The analysis can be generalized. We considered just one space-time sheet, the one swept out through time by the hole we imagined drilled through the earth. Nothing in the analysis depended upon where we drilled the hole. We could have drilled many holes.

Each would sweep out a different sheet in spacetime to which this analysis would apply. In general, there are three independent spatial directions we could have chosen, correspondingly to the three axes of a three dimensional space.

Finding the curvature in the three resulting sheets would be enough to fix the curvature in all possible sheets generated by holes we may dig. One special fact about gravity makes it an especially apt redescription. There is a uniqueness in free fall trajectories that is peculiar to gravity.

If we drop a one pound ball in the tube, it will take 42 minutes to pass to the other side of the earth. The same is true of a two pound ball; or a three pound ball; or a ball of any mass. They all take 42 minutes to pass to the other side of the earth. While they do it, they follow exactly the same trajectory. So if we release a one, two and three pound ball at the same moment, they will remain together as they traverse the hole to the other side.

This is the uniqueness of free fall. In Newtonian theory, the result is given more complicated expression. The quantity that measures how much gravitational force will act on a body in some gravitational field is its gravitational mass.

The quantity that measures how much a given body will accelerate when acted on by a force is the body's inertial mass. It is an unexplained coincidence in Newtonian theory that these two masses are equal. The result is the uniqueness of free fall. If electric forces were pulling the balls through the tube, this uniqueness of fall would fail. There is no coupling of inertial mass and electric charge. So if we drop one body which carries twice the charge of a second, there is no assurance that the inertial mass is also doubled; and so no assurance that the two will fall alike.

This remarkable result of the uniqueness of free fall is what makes the reinterpretation very comfortable. We can think of the spacetime sheet as having a natural spacetime geometry revealed to us by masses. That geometry is largely independent of the test masses that fall within it. All masses--big and small--reveal the same trajectories. The masses are more like probes exploring an independently existing structure.

It is as if we can see trains moving at night or in dim light. If we didn't know how trains worked, we might be puzzled that they all follow the same paths.

But when the light comes, we can see that there are railroad tracks covering the ground and that the trains merely follow them.

We can use them as probes in the dark that reveal where the tracks lie. Finally Einstein's reinterpretation eradicates an awkwardness of Newtonian theory. That theory had to posit that increases in gravitational mass in bodies are perfectly and exactly compensated by corresponding increases in inertial mass, so that the uniqueness of free fall can be preserved. Einstein's redescription does away with that coincidence and even the very idea of distinct inertial and gravitational masses.

In his theory, bodies now just have mass, or, in the light of special relativity, mass-energy. For Einstein the primitive notion is the geometrical structure of spacetime with the curved trajectories traced out by all freely falling bodies, independently of their mass. So far, we have dealt with an especially simple case in which the curvature of the space-time sheet is everywhere the same.

More generally curvature in spacetime will vary from event to event and, even at one event, it will be different according to the particular space-time sheet considered. This is simply a re-expression in curvature language of the more familiar fact that gravitation varies from place to place and acts differently in different directions. We can explore this variability by considering masses falling under the action of gravity above the surface of the earth. As before, we will ignore the rotation of the earth.

To begin, consider masses miles above the surface, stacked up 1 mile apart as shown and initially at rest with respect to earth. Now let them fall freely. The masses closer to the earth will feel a slightly stronger pull of gravity, so they will fall slightly faster. It is easy to compute the effect. In the course of A mass that is one mile closer, however, will fall 1.

If we plot these motions through time on a spacetime diagram, we recover a familiar figure. This is just a space-time sheet showing diverging trajectories; that is, this particular space-time sheet has negative curvature. We will get a different outcome if we consider masses aligned horizontally. Back to top. Learn about:. What the theories of general and special relativity say What the difference is between the two Practical applications of the theory Why did the apparent faster than light neutrinos challenge this theory?

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