Curvature without tidal forces

In summary, curvature without tidal forces is the bending of space caused by a massive object without any additional effects from gravity or tidal forces. This is different from general relativity, which considers the effects of matter and energy on the curvature of space. It can be observed in real life through phenomena such as gravitational lensing. Curvature without tidal forces affects the path of objects in space, causing them to follow a curved trajectory, and it is important for our understanding of the universe and the behavior of massive objects.
  • #1
Ratzinger
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How is spacetime curved if the present gravity field is completely uniform and there are no tidal forces. Clocks at a same height would tick the same, at different heights (to the gravity source) would tick differently. But what about space? How is space curved in the absence of tidal forces?

Often curvature is introduced with falling elevators without tidal forces. The observer in a falling elevator sees a light ray going from on side of the elevator wall to the other as a straight line. An outside observer sees a bended line. Thus gravity bends spacetime they say. Later then tidal forces and the non-uniformity of gravity fields is mentioned and made responsible for curvature.

So again my question: how would space be bent in a complete uniform gravity space?

thank you
 
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  • #2
In a completely uniform gravitational field, it's my understanding that spacetime would be flat. For example, this page on the twin paradox in flat spacetime mentions that you can understand things from the point of view of the accelerated twin by introducing a uniform gravitational field during the period of acceleration...but the curvature of spacetime is supposed to be independent of your coordinate system, so if the inertial twin sees spacetime as flat throughout the journey, then the accelerating twin should see the same thing.
 
  • #3
Ratzinger said:
How is spacetime curved if the present gravity field is completely uniform and there are no tidal forces. Clocks at a same height would tick the same, at different heights (to the gravity source) would tick differently. But what about space? How is space curved in the absence of tidal forces?

Often curvature is introduced with falling elevators without tidal forces. The observer in a falling elevator sees a light ray going from on side of the elevator wall to the other as a straight line. An outside observer sees a bended line. Thus gravity bends spacetime they say. Later then tidal forces and the non-uniformity of gravity fields is mentioned and made responsible for curvature.

So again my question: how would space be bent in a complete uniform gravity space?

thank you

If you have a flat Minkowski space-time, the curvature tensor is zero, and this will be true regardles of the coordinate system used.

However, if you adopt non-inertial coordinates to describe a flat minkowskian space-time, like the coordinate system of an accelerated observer, you can make the Chirsotffel symbols non-zero, even though you can never make the curvature tensor non-zero.

Non-zero Christoffel symbols can cause, for instance, the opposite sides of a parallelogram to have different lengths. This is somtimes called "curvature", but that's really speaking very losely. It's quite commonly done, though, including in many textbooks.
 
  • #4
Ratzinger said:
How is spacetime curved if the present gravity field is completely uniform and there are no tidal forces. Clocks at a same height would tick the same, at different heights (to the gravity source) would tick differently. But what about space? How is space curved in the absence of tidal forces?

Often curvature is introduced with falling elevators without tidal forces. The observer in a falling elevator sees a light ray going from on side of the elevator wall to the other as a straight line. An outside observer sees a bended line. Thus gravity bends spacetime they say. Later then tidal forces and the non-uniformity of gravity fields is mentioned and made responsible for curvature.

So again my question: how would space be bent in a complete uniform gravity space?

thank you
At one time (before I learned GR) I wondered about this too so after I learned GR I wrote up the answers to your question in this article

http://xxx.lanl.gov/abs/physics/0204044

Pete
 
  • #5
As already mentioned, there is no spacetime curvature with a uniform gravitational field. The modern interpretation is that things "fall" in such fields due to the observer's nonzero (4-)acceleration (the magnitude of which is an invariant), and that it really isn't a gravitational effect.

Of course other interpretations are possible - and are occasionally convenient - but this one tends to be the most foolproof. Relying on nonvanishing Christoffel symbols is a great way to confuse yourself. Even the physicists working on GR were confused by it (and similar ideas) back when such statements were still popular. Hardly anyone made any progress in the field until the old coordinate-dependent notions were removed from everyones' minds. That took about 40 years.
 

1. What is curvature without tidal forces?

Curvature without tidal forces refers to the bending of space caused by the presence of a massive object, such as a planet or star, without any additional effects from gravitational pull or tidal forces.

2. How is curvature without tidal forces different from general relativity?

General relativity is a theory that describes the curvature of space and how it is affected by the presence of matter and energy. Curvature without tidal forces is a specific case in which only the bending of space is considered, without any additional effects from gravity or tidal forces.

3. Can curvature without tidal forces be observed in real life?

Yes, curvature without tidal forces can be observed in the bending of light around massive objects, such as stars. This is known as gravitational lensing and has been observed and studied by astronomers.

4. How does curvature without tidal forces affect objects in space?

Curvature without tidal forces can affect the path of objects in space, causing them to follow a curved trajectory around a massive object. This effect is known as geodesic deviation and is a fundamental concept in the theory of general relativity.

5. Is curvature without tidal forces important for our understanding of the universe?

Yes, the concept of curvature without tidal forces is important in our understanding of the universe and the behavior of massive objects in space. It is a key aspect of general relativity and helps us explain phenomena such as gravitational lensing and the motion of planets and stars in the universe.

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