# Thread: Do things move relatively to the spacetime manifold ?

1. According to Special Relativity, there is no 'medium' to refer motion to.
Hence the equivalence principle.

Then GR introduces a spacetime manifold, the curvage of spacetime, the fabric of spacetime, the Riemann tensor, to account for a gravity-system.

> Are things in many cases not moving relative then to this spacetime ?  2.

3. Originally Posted by Noa Drake Are things in many cases not moving relative then to this spacetime ?
No, because "space-time" is not a valid frame of reference. While the geometric objects defined on the manifold ( i.e. the metric tensor and the curvature tensors, among others ) are independent of the observer, their component representations are explicitly dependent on a choice of coordinate basis - which is entirely arbitrary. In fact, since the manifold incorporates both space and time, as well as everything in it, it is completely static - things aren't described by their motion, but by the geometry of their static world lines.  4. I understand the setup there, but it is selfimposing a number of things to agree on, no ?

I am referring to the idea of a discrete spacetime where objekts would move relatively to 'spacetime', this would not destroy the predicted behaviour of objekts.
Nor would it destroy the notion of an apparently continuous spacetime having certain characteristics.  5. Originally Posted by Noa Drake I am referring to the idea of a discrete spacetime where objekts would move relatively to 'spacetime'
Space-time is just a way of describing the relationships (distances, and the geometry of those distances) between objects and events. It is not a fixed "grid" that things move relatively to.

What you are asking is a bit like saying, "do objects move relative to the kilometre and the second".  6. General relativity is a field theory. Fields are mathematical functions of the coordinates of spacetime such as: (Note: the numerical superscripts simply label the coordinates, they are not exponents.)

This is in contrast to mechanics where the coordinates of an object are mathematical functions of one or more parameters, such as:    (In this example, there is one parameter, , and therefore the above set of equations describe a one-dimensional curve in spacetime,)  7. Ok, but isn't it questionable that we have to say it is theoretical when asked if it is real and to be related to on one hand,
and then again to say that it is very real when having to account for objekts to stay in a gravitational condition the way they do ?
I mean these objekts are experiencing a fysical encounter with 'the item' that keeps them in place, no ?  8. Originally Posted by Noa Drake I mean these objekts are experiencing a fysical encounter with 'the item' that keeps them in place, no ?
A point object in a non-zero gravitational field has a straight line trajectory in spacetime, just as it would in zero gravitational field. Thus, the gravitational field doesn't have any affect on a point object. Spacetime curvature does alter what it means to be a straight line globally, but locally a straight line in curved spacetime has the same meaning as it does in flat spacetime. Spacetime curvature does produce tidal effects that affect extended objects (but not point objects).  9. Originally Posted by KJW General relativity is a field theory. Fields are mathematical functions of the coordinates of spacetime such as: (Note: the numerical superscripts simply label the coordinates, they are not exponents.)
An important (perhaps the most important) aspect of general relativity is that the coordinate system used to describe the fields are arbitrary. Thus, one can transform to a different coordinate system:    Substituting into , one obtains: which is a function of the new coordinates: Note that and describe the same field, even though the descriptions are different due to being in terms of a different coordinate system.  10. Originally Posted by Noa Drake I mean these objekts are experiencing a fysical encounter with 'the item' that keeps them in place, no ?
Space time is no more an "item" that holds things in place than the equator is.  Bookmarks
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