• B
• UfoPilot
In summary: In particular, the 4-d world tubes of the 2 satellites are different (world tubes in GR being the 4-d generalization of world lines in SR). So, yes, each satellite has its own "locally" flat 4-d geometry, but these 4-d geometries are different from each other, and in fact are not really "the same" in the sense that they cannot be smoothly connected to each other (imagine trying to merge the two world tubes together into one smooth world tube).In summary, the conversation discusses how the geometry of space-time curvature is affected by the presence of matter and energy. Space-time is not the same as space, and the curvature can change depending on the relative motion of objects.
UfoPilot
please help me understand this, space is flat. space bends when its near matter. When matter moves from point A to point B, the space at point A returns to being flat. Where does the energy come from to bend the space back to flat come from? Why doesn't the space at point A stay bent?

UfoPilot said:
The geometry of space-time curvature would indeed be flat if no energy was present anywhere.
UfoPilot said:
space bends when its near matter
This geometry indeed change with respect to the many component of that matter/energy (See stress energy tensor)

UfoPilot said:
When matter moves from point A to point B, the space at point A returns to being flat.
That's correct, the curvature is mostly dependent on distance.

UfoPilot said:
Where does the energy come from to bend the space back to flat come from?
No energy is used to affect that curvature. Only in very extreme cases (like black holes merging) some energy is indeed transferred to that curvature and in the forms of gravitational waves.

UfoPilot said:
Why doesn't the space at point A stay bent?
For the same reason it was flat in the first place.
Also, that curvature is different for every object depending on their relative motion. For example take a snapshot of two identical satellite nearly at the same point in space. If one is going at great speed horizontally, it will "follow" and orbital (but also free fall) geometry. If one is dropped at zero velocity there (also with respect to earth) it will make the apple free fall dive. So despite (nearly) being at the same place (in space), they both will experience a totally different (4 dimensional) geometry (Nothing happens to space itself).

That's why it is also said that in GR space time curvature guide object into free fall along their "straight line" geodesics

UfoPilot said:
space is flat

What "space" are you talking about? Are you talking about our universe as a whole? That is spatially flat, yes (according to your best current model). But "space" without qualification is too vague.

UfoPilot said:
space bends when its near matter.

No, spacetime is curved when matter and energy is present. Spacetime is not the same thing as space.

UfoPilot said:
When matter moves from point A to point B, the space at point A returns to being flat.

No; when matter moves from point A to point B, spacetime is more curved in the 4-dimensional region that includes the "world tube" between A and B that the matter occupies, and less curved far away from that region. Nothing "returns to being flat"; spacetime, as a 4-dimensional manifold, does not "change", it just is. What we think of as "change" in our everyday world, in the 4-d spacetime model is just the geometry being different in some regions vs. others.

UfoPilot said:
Where does the energy come from to bend the space back to flat come from?

It doesn't have to come from anywhere. See above.

Boing3000 said:
that curvature is different for every object depending on their relative motion.

This is not true. The Riemann curvature tensor, which describes spacetime curvature, is a tensor, i.e., a covariant geometric object. It is the same tensor for every observer, whatever their state of motion.

Boing3000 said:
take a snapshot of two identical satellite nearly at the same point in space. If one is going at great speed horizontally, it will "follow" and orbital (but also free fall) geometry. If one is dropped at zero velocity there (also with respect to earth) it will make the apple free fall dive. So despite (nearly) being at the same place (in space), they both will experience a totally different (4 dimensional) geometry

This is not correct. Both satellites are moving through the same 4-d geometry. They are just moving on different geodesics in that same 4-d geometry.

## 1. What is space bending?

Space bending is a concept in theoretical physics that involves manipulating the fabric of space-time. It suggests that it is possible to bend or warp the space around an object, causing it to move in a different path or creating a gravitational pull.

## 2. How does space bending work?

Space bending works by altering the space-time continuum, which is the fabric of the universe that includes three dimensions of space and one dimension of time. This can be achieved through the use of massive objects, such as planets or stars, which have a strong gravitational pull and can bend the space around them.

## 3. Is space bending possible?

While space bending is a theoretical concept, it has not yet been proven to be possible. Scientists are still conducting research and experiments to better understand the laws of the universe and the potential for space bending.

## 4. What are the potential applications of space bending?

If space bending were to be proven possible, it could have a variety of applications in space travel and exploration. It could potentially allow for faster-than-light travel, making it possible to reach distant planets and galaxies in a shorter amount of time. It could also be used for creating artificial gravity in space habitats.

## 5. How does space bending relate to Einstein's theory of relativity?

Space bending is closely related to Einstein's theory of relativity, specifically the concept of general relativity. This theory suggests that gravity is not a force between masses, but rather a curvature of space and time caused by the presence of massive objects. This aligns with the idea of space bending as a way to manipulate the fabric of space-time.

• Special and General Relativity
Replies
21
Views
4K
• Special and General Relativity
Replies
8
Views
1K
• Special and General Relativity
Replies
2
Views
1K
• Special and General Relativity
Replies
34
Views
491
• Special and General Relativity
Replies
14
Views
1K
• Special and General Relativity
Replies
13
Views
1K
• Special and General Relativity
Replies
81
Views
8K
• Special and General Relativity
Replies
27
Views
4K
• Special and General Relativity
Replies
15
Views
2K
• Special and General Relativity
Replies
16
Views
1K