Inertial reference frames

In summary, there are two ways to create a local inertial reference frame in a gravitational field: by creating a small frame close to the source of curvature, or by creating a large frame far from the source. If the reference frame has mass, it becomes a source of curvature and cannot be separated from it. While there is no readily available quantitative relationship in general relativity, it is possible to calculate one if ambitious enough.
  • #1
kurious
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I can make a local inertial reference frame in a gravitational field by creating a frame that is small but close to the source of curvature of space-time.
Alternatively I can make a local inertial reference frame by creating a frame that is large but a long distance from the source of curvature of space-time.
If the reference frame has a mass, is there a quantitative relationship in general relativity between the mass/size of the frame and its distance from the source of curvature of space-time?
 
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  • #2
If the reference frame has a mass, then it IS a source of curvature, and cannot be separated from that.
 
  • #3
kurious said:
I can make a local inertial reference frame in a gravitational field by creating a frame that is small but close to the source of curvature of space-time.
Alternatively I can make a local inertial reference frame by creating a frame that is large but a long distance from the source of curvature of space-time.
If the reference frame has a mass, is there a quantitative relationship in general relativity between the mass/size of the frame and its distance from the source of curvature of space-time?

Not one that is readily available but if one is ambitious it can be calculated. I'm not that ambitious though. :-)

Pete
 

1. What is an inertial reference frame?

An inertial reference frame is a coordinate system used to describe the motion of objects in space. In this frame, Newton's first law of motion holds true, stating that objects at rest will remain at rest and objects in motion will continue in a straight line at a constant speed unless acted upon by an external force.

2. How is an inertial reference frame different from a non-inertial reference frame?

An inertial reference frame is a frame of reference that is not accelerating or rotating, while a non-inertial reference frame is accelerating or rotating. In an inertial reference frame, objects will appear to obey Newton's laws of motion, while in a non-inertial reference frame, fictitious forces may need to be introduced to explain the motion of objects.

3. What is the importance of using an inertial reference frame in scientific experiments?

Using an inertial reference frame allows for accurate and consistent measurements and observations of motion. It eliminates the need to account for additional forces that may be present in a non-inertial reference frame, making it easier to analyze and understand the behavior of objects.

4. How do we determine if a reference frame is inertial?

A reference frame is considered inertial if Newton's first law of motion holds true within that frame. This can be determined by observing if objects at rest remain at rest and objects in motion continue in a straight line at a constant speed, without the need for additional forces to explain their motion.

5. Can we always use an inertial reference frame in scientific experiments?

No, there are certain situations where an inertial reference frame may not be appropriate. For example, when studying the motion of objects in a rotating reference frame, it may be necessary to use a non-inertial reference frame to accurately describe their motion. Additionally, in situations where the effects of gravity are significant, an inertial reference frame may not be suitable.

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