Generating a curved spacetime environment

[geordief]

Suppose one creates artificial gravity  in a rotating space craft, is it possible to  show that geometry aboard the craft has been curved?

 

For instance if there were different decks representing different gravity levels and students (on different decks) were to  be doing regular (Euclidean) geometry lessons on graph paper  with gridlines that they  had made themselves, would the otherwise identical drawings appear the same when they were compared side by side at a later date?

 

Would it be possible  to say ,by looking at the drawings on which deck the drawings had been made? Or would perhaps the drawings need to be animated for this to be possible? 

[beecee]

8 minutes ago, geordief said:

Suppose one creates artificial gravity  in a rotating space craft, is it possible to  show that geometry aboard the craft has been curved?

 

For instance if there were different decks representing different gravity levels and students (on different decks) were to  be doing regular (Euclidean) geometry lessons on graph paper  with gridlines that they  had made themselves, would the otherwise identical drawings appear the same when they were compared side by side at a later date?

 

Would it be possible  to say ,by looking at the drawings on which deck the drawings had been made? Or would perhaps the drawings need to be animated for this to be possible? 

A rotating space craft, say like the famous space wheel in "2001: A Space Odyssey" would have gravity around the rim, at a level akin to Earth's surface gravity [9.8 mts/S2] and that gravity falling off approaching  zero as one  reached the center. But that doesn't answer your question/s, sorry. 

[swansont]

36 minutes ago, geordief said:

Suppose one creates artificial gravity  in a rotating space craft, is it possible to  show that geometry aboard the craft has been curved?

 

For instance if there were different decks representing different gravity levels and students (on different decks) were to  be doing regular (Euclidean) geometry lessons on graph paper  with gridlines that they  had made themselves, would the otherwise identical drawings appear the same when they were compared side by side at a later date?

 

Would it be possible  to say ,by looking at the drawings on which deck the drawings had been made? Or would perhaps the drawings need to be animated for this to be possible? 

How big is the graph paper? Locally spacetime will be flat.

You could show that there are relativistic effect by looking at clock signals. Syntonized clocks will have different frequencies when moved to other decks.

If you are spinning fast enough, an external observer would see the circumference be off. But you can't actually spin fast enough for this to be easily measurable. 
https://en.wikipedia.org/wiki/Ehrenfest_paradox

[geordief]

19 minutes ago, swansont said:

How big is the graph paper? Locally spacetime will be flat.

You could show that there are relativistic effect by looking at clock signals. Syntonized clocks will have different frequencies when moved to other decks.

If you are spinning fast enough, an external observer would see the circumference be off. But you can't actually spin fast enough for this to be easily measurable. 
https://en.wikipedia.org/wiki/Ehrenfest_paradox

Well suppose we  made the graph paper  big enough** would the students' ("students" for realistic effect:it could be machines) efforts be distinguishable according to the different levels of the artificial gravity "well" they were situated in?

How would the students (or machines) draw their gridlines according to what they perceived as Euclidean principles (without using readymade rulers?) Draw two points ,join the dots and extend the line in the same direction? Then construct perpendiculars and you have the graph paper....

Then compare results from different levels ...... would there be any perceptible difference in the "straight lines" from one drawing to another?

 

**I mean size would be unlimited ,especially if the "students" are replaced with drawing machines.

 

 

[swansont]

27 minutes ago, geordief said:

Well suppose we  made the graph paper  big enough** would the students' ("students" for realistic effect:it could be machines) efforts be distinguishable according to the different levels of the artificial gravity "well" they were situated in?

How would the students (or machines) draw their gridlines according to what they perceived as Euclidean principles (without using readymade rulers?) Draw two points ,join the dots and extend the line in the same direction? Then construct perpendiculars and you have the graph paper....

Then compare results from different levels ...... would there be any perceptible difference in the "straight lines" from one drawing to another?

 

**I mean size would be unlimited ,especially if the "students" are replaced with drawing machines.

Think about this: You have people on earth and on a spaceship. Would drawings made on them differ from each other because the spaceship was moving at high speed, and then returned to the earth? No. Locally everything is normal. Even though we would observe length contraction, everything is shrunk, so the size of an object drawn on the graph paper shrinks in the same proportion as the grid lines. A 2 x 2 square that is drawn is still 2 x 2, even if the stationary observer measures it as 1 x 1.

Similarly, we see curved spacetime only as a distant observer. We see e.g. a curved path for light because we are in a different curvature. Locally everything is flat. Anyone drawing a straight line 1 cm in length can compare it side-by-sude to anyone else's drawing and that's what it will be, but if you observe it from a distance (a different frame) you will see it is curved and/or not 1 cm

[koti]

I have a related question...if we set the mass of that rotating space station from Space Odyssey 2001 to a certain value large enough which would enable the system to rotate at less than c, would the system be able to rotate itself into a singularity?

[geordief]

6 minutes ago, swansont said:

Think about this: You have people on earth and on a spaceship. Would drawings made on them differ from each other because the spaceship was moving at high speed, and then returned to the earth? No. Locally everything is normal. Even though we would observe length contraction, everything is shrunk, so the size of an object drawn on the graph paper shrinks in the same proportion as the grid lines. A 2 x 2 square that is drawn is still 2 x 2, even if the stationary observer measures it as 1 x 1.

Similarly, we see curved spacetime only as a distant observer. We see e.g. a curved path for light because we are in a different curvature. Locally everything is flat. Anyone drawing a straight line 1 cm in length can compare it side-by-sude to anyone else's drawing and that's what it will be, but if you observe it from a distance (a different frame) you will see it is curved and/or not 1 cm

I see. There is zero difference between drawings made in zero g environments and drawings made on the Earth  for example,no matter how large  the drawings? 

 

[swansont]

15 minutes ago, geordief said:

I see. There is zero difference between drawings made in zero g environments and drawings made on the Earth  for example,no matter how large  the drawings? 

I can't think of a reason (from relativity) why there would be.

[geordief]

Just now, swansont said:

I can't think of a reason (from relativity) why there would be.

Would (large) drawings on Earth  not use lines very close to the lines we see on a map of the globe  whilst parallel lines drawn in Space would only meet at greatly increased distances? 

[swansont]

2 minutes ago, geordief said:

Would (large) drawings on Earth  not use lines very close to the lines we see on a map of the globe  whilst parallel lines drawn in Space would only meet at greatly increased distances? 

That's a question of how the paper is manufactured. It is also not a relativistic effect.

[geordief]

1 minute ago, swansont said:

That's a question of how the paper is manufactured. It is also not a relativistic effect.

Could the paper be manufactured at the same time the lines were drawn (made to measure )

 

The paper would be judged "straight" in the same way the lines were "straight" Maybe manufacturing "straight" paper is just as  important as making drawings......

 

Why is this not a relativistic effect if we are talking about gravity or curved spacetime?