# Thread: Space is curved relative to what?

1. Spacetime, as I understand it, is curved. This may one day allow us to build a wormhole shortcut from one part of space to the other. I once saw a diagram of Manhattan. One end curled back so that the north side of Manhattan was just above the south side. We were told to imagine that Manhattan was curved space and that a tunnel (wormhole) could be built from the south side directly up to the north side. OK, but:

1. If spacetime is curved, what is it curved relative to? If someone on the north side of Manhattan starts walking south, they'll eventually get to the south side and feel like they went straight the whole time. If we can't see that space is curved from within space, what is the place where we can see it curved?

2. Same question: What does the wormhole go through? If it's connecting two parts of space, then it is not going through space. It's going through something else. What is that something else?

3. Same question: When Manhattan curls back, what does it curl back through?

Thanks!

2.

3. The difference is between intrinsic curvature and extrinsic curvature.

If you had a balloon, then the 2D surface could easily be seen to curved if view from our 3D perspective. Also, a 2D creature living in the 2D plane surface of the balloon might be living in a universe that is curved in the 2 dimensions he lives in and can perceive, yet a 3'rd exists in which it is curved. Such a setup where curvature in a certain number of dimensions need an extra dimension to describe that curvature is extrinsic curvature.

Thing is, that extra dimension is not necessary to describe curvature. Curvature in a number of dimensions that need only those number of dimension to describe it's curvature is intrisic curvature. Without worrying about string theory, that is the type of universe that is describable with general relativity, where only 3 spatial and 1 time dimension exists, but where curvature is describable by those 4 dimensions that we can perceive. No extra dimensions are needed.

I was with you when you were making the point that the place where you could see the curvature of a 3D space would be in a higher dimension, but you lost me when you made the point that it has nothing to do with dimensions. That curvature is intrinsic. How is that? If space has curvature, that means that light travels along that curvature, isn't that right? So, if I extend my arms out in front of me, they will actually curve up, but so will light. So, to me, it will seem that my arms are always straight! I can't see how I might see the curvature of a 3D space from within it. Is there an example or analogy to describe this?

5. Originally Posted by PaulPSA

1. If spacetime is curved, what is it curved relative to? If someone on the north side of Manhattan starts walking south, they'll eventually get to the south side and feel like they went straight the whole time. If we can't see that space is curved from within space, what is the place where we can see it curved?
Great question to ask. Definitely shows you understand relativity. Everything depends on who's observing.

2. Same question: What does the wormhole go through? If it's connecting two parts of space, then it is not going through space. It's going through something else. What is that something else?
The worm hole is made of space. It is the space. If it's connecting two points in space, what that really means is that those two points in space are touching.

3. Same question: When Manhattan curls back, what does it curl back through?

Thanks!
What does the Earth curl around through? If you start on the equator and walk due East, eventually you'll end up where you started.

If Manhattan were curved via a wormhole, I think it would not be much different.

6. If human get success in the curve of space then it is sure thing that the space journey will become short.

7. If spacetime is curved, what is it curved relative to?
Curvature is an intrinsic property of space-time; it is defined via the notion of "parallel transport" on a manifold, and not with reference to some other "outside" state. The question is thus meaningless, it is not curved relative to anything else.

Also bear in mind that space-time is not a valid frame of reference.

8. Originally Posted by PaulPSA
....1. If spacetime is curved, what is it curved relative to? .....
According to General Relativity (GR) you can consider spacetime as completely flat, meaning that there is no curvature to it at all. But in the presence of matter supposedly spacetime curves surrounding matter. Considering the mass of the universe as a whole, spacetime could accordingly curve around upon itself closing space concerning its volume. This is the current thought and idea of your Manhattan analogy but not the only possibility according to GR. So far observations have indicated that observable space in completely flat within the limits of present detection. If the curved space concept of GR is wrong then spacetime might be a far simpler concept.

9. Forrest... what?!

Spacetime is definitely curved around here, otherwise you wouldn't be sitting in your chair.

You seem to be conflating local curvature (matter tells spacetime how to curve and spacetime tells matter how to move) with the concept of global curvature (do we live in a flat universe or not?). These are not the same thing.

10. Originally Posted by SpeedFreek
Forrest... what?!

Spacetime is definitely curved around here, otherwise you wouldn't be sitting in your chair.

You seem to be conflating local curvature (matter tells spacetime how to curve and spacetime tells matter how to move) with the concept of global curvature (do we live in a flat universe or not?). These are not the same thing.
Yes, if the concepts of GR are correct then local space curves, if not (dare I say) then space may not curve If the observable universe as a whole appears to be flat, this does not preclude the possibility of it curving as a whole, at a much larger scale.

11. Both "space" and "time" are imaginary coordinate systems with utterly no empirical referent. They can not be affected by anything real and have no effect on reality.

12. Originally Posted by Plautus
Both "space" and "time" are imaginary coordinate systems with utterly no empirical referent. They can not be affected by anything real and have no effect on reality.
Ok then - since coordinate systems have no effect on reality, then perhaps you could demonstrate how to set up your next, say, job interview without reference to any space or time coordinates.
Good luck

13. I'm not sure exactly what you mean there, Plautus.

Space and time are definitely affected by anything real. This is the basis of both kinetic and gravitational time-dilation, which are well established and well tested principles - the GPS system would not work properly without them.

14. He's trolling several threads, making bold claims, refusing flatly to support them and ignoring all evidence presented. Sometimes, a person like that is useful since they present the opportunity to teach the silent readers... But this one posts heavily and the threads will grow too lengthy, too quickly, for a silent reader to bother following. It's more likely he'll drive others to ad homs, than inspire anyone for any reason.

I suggest reporting him and letting him froth at the mouth by himself.

Just waiting for the inevitable...

16. Originally Posted by Markus Hanke
Originally Posted by Plautus
Both "space" and "time" are imaginary coordinate systems with utterly no empirical referent. They can not be affected by anything real and have no effect on reality.
Ok then - since coordinate systems have no effect on reality, then perhaps you could demonstrate how to set up your next, say, job interview without reference to any space or time coordinates.
Good luck
Do you really not understand that both "space" and "time" are just imaginary coordinate systems? If you think "space" is real, go grab some of it and try to bend it. It's laughable on its face. That you accept it without question demonstrates your inability to distinguish between reality and the imaginary.

17. Originally Posted by SpeedFreek
I'm not sure exactly what you mean there, Plautus.

Space and time are definitely affected by anything real.
Both "space" and "time" are imaginary coordinate systems, not something real.

Originally Posted by SpeedFreek
This is the basis of both kinetic and gravitational time-dilation, which are well established and well tested principles - the GPS system would not work properly without them.
GPS technology does not rely on the concept of "curved space" being valid to function. Like so many other people you believe that it does. This demonstrates your loose grip on reality. Perhaps if you actually studied science instead of reading some blogs you would be less superstitious.

18. Originally Posted by Plautus
Do you really not understand that both "space" and "time" are just imaginary coordinate systems? If you think "space" is real, go grab some of it and try to bend it. It's laughable on its face. That you accept it without question demonstrates your inability to distinguish between reality and the imaginary.
You did not answer my question, Mr Troll. Please uniquely identify an event for me without reference to space and time.

19. Originally Posted by Neverfly
He's trolling several threads, making bold claims, refusing flatly to support them and ignoring all evidence presented. Sometimes, a person like that is useful since they present the opportunity to teach the silent readers... But this one posts heavily and the threads will grow too lengthy, too quickly, for a silent reader to bother following. It's more likely he'll drive others to ad homs, than inspire anyone for any reason.

I suggest reporting him and letting him froth at the mouth by himself.
You have not even made any assertions let along presented any evidence of anything except your tendency to be insulting and wander off topic with your random speculations about other people. I see in this thread you also offer nothing but your libelous statements and proud ignorance.

20. Originally Posted by Markus Hanke
You did not answer my question, Mr Troll.
You did not cup my balls, Mr. Cocksucker.

Originally Posted by Markus Hanke
Please uniquely identify an event for me without reference to space and time.
You do understand reality would still exist even if you could not describe it.

21.

22. Originally Posted by Plautus
Originally Posted by Markus Hanke
You did not answer my question, Mr Troll.
You did not cup my balls, Mr. Cocksucker.

Originally Posted by Markus Hanke
Please uniquely identify an event for me without reference to space and time.
You do understand reality would still exist even if you could not describe it.
Reported for profanity and trolling.

23. Originally Posted by Dywyddyr
Just waiting for the inevitable...
Has anyone reported you for using an angry duck cartoon avatar? I've noticed the tendency of irrational people to gravitate toward cartoon avatars and other fantastical nonsense like anime characters with huge swords (overcompensate much?) or bitter and stubbornly stupid cartoon ducks.

24. And you still have not answered my question.

25. Originally Posted by Plautus
GPS technology does not rely on the concept of "curved space" being valid to function. Like so many other people you believe that it does. This demonstrates your loose grip on reality. Perhaps if you actually studied science instead of reading some blogs you would be less superstitious.
Utter nonsense on your part. We had to factor in the predicted time-dilations from both Special Relativity and General Relativity when setting the clock speeds on the GPS satellites, before they were launched, in order for those GPS satellite clocks to be synchronised with clocks on the surface on the Earth, due to both the relative speed of a GPS satellite when compared to a clock on the surface of the Earth and the difference in gravitational potential between the surface of the Earth and the orbital radius of the aforementioned satellites.

This is a fact.

We even have a member here who worked on the GPS system and will confirm this.

So why are you spreading this nonsense? What do you hope to achieve by propagating anti-knowledge?

26. Originally Posted by Markus Hanke
Originally Posted by Plautus
Originally Posted by Markus Hanke
You did not answer my question, Mr Troll.
You did not cup my balls, Mr. Cocksucker.

Originally Posted by Markus Hanke
Please uniquely identify an event for me without reference to space and time.
You do understand reality would still exist even if you could not describe it.
Reported for profanity and trolling.
And you're reported for being a little bitch. Anyone who cares to read the history will see you are the one trying to troll me. You've offered nothing regarding to the subject at hand, just a lot of random speculation about me, the same as a few other people who have been riding my nutsack since I first started posting. Don't delude yourself into thinking your troll mafia is anything but a group of misfit hermits.

27. Originally Posted by Plautus
and other fantastical nonsense like anime characters with huge swords (overcompensate much?)
It's true... black holes, anti-matter and Relativity are faith-based beliefs, 9-11 was an inside job and I'm marvelously under-endowed and drive a really big pick up truck.
Originally Posted by Plautus
who have been riding my ******* since I first started posting.
Almost 50 posts in less than two hours...

28. Originally Posted by SpeedFreek
So why are you spreading this nonsense?
Because he's a troll.

29. Originally Posted by Markus Hanke
And you still have not answered my question.
You have yet to formulate a sensible question that has any relevance to the subject at hand.

30. Originally Posted by Plautus
And you're reported for being a little bitch. Anyone who cares to read the history will see you are the one trying to troll me. You've offered nothing regarding to the subject at hand, just a lot of random speculation about me, the same as a few other people who have been riding my nutsack since I first started posting. Don't delude yourself into thinking your troll mafia is anything but a group of misfit hermits.
Reported again

31. Originally Posted by Plautus
You have yet to formulate a sensible question that has any relevance to the subject at hand.
The subject is your assertion that space and time have no physical reality. The question is to hence uniquely identify an event without reference to space and time. That is quite sensible.

32. So, Plautus, how do you account for the FACT that the clocks on GPS satellites act exactly as Einstein predicted?

Or how do you account for the results of the Hafele-Keating experiment? (which has been performed repeatedly and proves the time-dilation)

Oh, and by the way, science is true whether you believe in it, or not.

33. Originally Posted by SpeedFreek
Utter nonsense on your part. We had to factor in the predicted time-dilations from both Special Relativity and General Relativity when setting the clock speeds on the GPS satellites, before they were launched, in order for those GPS satellite clocks to be synchronised with clocks on the surface on the Earth, due to both the relative speed of a GPS satellite when compared to a clock on the surface of the Earth and the difference in gravitational potential between the surface of the Earth and the orbital radius of the aforementioned satellites.
You have no idea what you're talking about. GPS technology does not work as you describe, and you take no part in it, which explains your complete and total lack of understanding of it. GPS technology relies on and only on simple geometric triangulation. There aren't any "time dilation" effects that are factored into that procedure. No known technology relies on the notion of "curved space" having any validity whatsoever. That clocks function differently in different environments is not proof of this patently stupid idea of "curved space". Space is a virtual coordinate system, and so is time, neither has any empirical referent of any kind. Your inability to distinguish between real and imaginary is common to people who also have many faith-based beliefs.

34. Originally Posted by Neverfly
Originally Posted by Plautus
and other fantastical nonsense like anime characters with huge swords (overcompensate much?)
It's true... black holes, anti-matter and Relativity are faith-based beliefs, 9-11 was an inside job and I'm marvelously under-endowed and drive a really big pick up truck.
Originally Posted by Plautus
who have been riding my ******* since I first started posting.
Almost 50 posts in less than two hours...
You're not denying that you have a cartoon anime character as an avatar, are you. I don't think you need a degree in psychology to infer that you engage in flights of fancy, you are trying to project an imaginary persona to fit with your imaginary belief systems. Well done self-identifying.

35. GPS technology relies on and only on simple geometric triangulation. There aren't any "time dilation" effects that are factored into that procedure.
Thanks for that demonstration of total ignorance. Refer here :

http://www.usna.edu/Users/physics/mu...ions/TPT11.pdf

36. It always amazes me how those trolls come on here 100% convinced of their superiority, while in reality they have no understanding whatsoever of even the fundamentals of the topic at hand...
Hilarious...thanks for the laughs at least

37. Originally Posted by Plautus
Originally Posted by SpeedFreek
Utter nonsense on your part. We had to factor in the predicted time-dilations from both Special Relativity and General Relativity when setting the clock speeds on the GPS satellites, before they were launched, in order for those GPS satellite clocks to be synchronised with clocks on the surface on the Earth, due to both the relative speed of a GPS satellite when compared to a clock on the surface of the Earth and the difference in gravitational potential between the surface of the Earth and the orbital radius of the aforementioned satellites.
You have no idea what you're talking about. GPS technology does not work as you describe, and you take no part in it, which explains your complete and total lack of understanding of it. GPS technology relies on and only on simple geometric triangulation. There aren't any "time dilation" effects that are factored into that procedure. No known technology relies on the notion of "curved space" having any validity whatsoever. That clocks function differently in different environments is not proof of this patently stupid idea of "curved space". Space is a virtual coordinate system, and so is time, neither has any empirical referent of any kind. Your inability to distinguish between real and imaginary is common to people who also have many faith-based beliefs.
You Sir, are an idiot. Time-dilation as described by both General and Special Relativity had to be taken into account in the GPS system. There is no denying this.

Science is not based on faith, it is based on empirical evidence, you fool.

38. Originally Posted by Neverfly
Again, you're going to have to do more than read a blog post to catch up here. Space is a virtual coordinate system that human minds invented, it is not something real. You can not manipulate space in any fashion because it is wholly imaginary and space can have no effect of any kind on reality. Your inability to distinguish between imaginary and real is common to people with faith-based belief systems in which they are strongly emotionally invested.

39. Originally Posted by Plautus
Well done self-identifying.
Thanks. Considering how bass-ackwards everything else you've said is- that's a compliment for your to claim I'm something you imply is negative.
Originally Posted by Plautus
Again, you're going to have to do more than read a blog post to catch up here.
I did.
Your faith based denials of any evidence that refutes your assertions is the mark of belief, no matter how much denial and dishonesty you engage in.

40. Originally Posted by Markus Hanke
Originally Posted by Plautus
And you're reported for being a little bitch. Anyone who cares to read the history will see you are the one trying to troll me. You've offered nothing regarding to the subject at hand, just a lot of random speculation about me, the same as a few other people who have been riding my nutsack since I first started posting. Don't delude yourself into thinking your troll mafia is anything but a group of misfit hermits.
Reported again
You're being a little bitch again, also. Note the striking coincidence between you being a bitch and you filing reports on people you're trolling. Eat my ass, motherfucker.

41. Bye bye Plautus, you unhinged nutjob. Take your stupid elsewhere.

(I'm predicting the swift registration of a "new" user here, who will continue where he left off....)

42. Originally Posted by Plautus
You're being a little bitch again, also. Note the striking coincidence between you being a bitch and you filing reports on people you're trolling. Eat my ass, motherfucker.
This post speaks rather nicely for itself

43. And here, for the benefit of any doubters, is some more of the real science, a published and peer reviewed paper (not an internet blog!) in a reputable journal, by a real physicist, which speaks for itself:

Relativity in the Global Positioning System

Also, it should be noted that, as I already said, the member here known as Strange actually worked on the GPS system and can confirm the reality of all this.

44. Originally Posted by SpeedFreek
And here, for the benefit of any doubters, is some more of the real science, a published and peer reviewed paper (not an internet blog!) by a real physicist, which speaks for itself:

Relativity in the Global Positioning System

http://relativity.livingreviews.org/...003-1Color.pdf
Pfft, scientific propaganda!
For my next "trick" I'm going to prove that chickens are lords of the sea and are why all aquatic dinosaurs died out - the chickens hunted them down and ate them.

45. Originally Posted by forrest noble
Originally Posted by PaulPSA
....1. If spacetime is curved, what is it curved relative to? .....
According to General Relativity (GR) you can consider spacetime as completely flat, meaning that there is no curvature to it at all. But in the presence of matter supposedly spacetime curves surrounding matter. Considering the mass of the universe as a whole, spacetime could accordingly curve around upon itself closing space concerning its volume. This is the current thought and idea of your Manhattan analogy but not the only possibility according to GR. So far observations have indicated that observable space in completely flat within the limits of present detection. If the curved space concept of GR is wrong then spacetime might be a far simpler concept.

afaik it's about the universe being flat. someone meassured the angle/distance from the cmbr being at 1 position and then 6 months later; seeing it leads to a 180 degree triangle.

that has nothing to do with mass curving/bending space ... and imo only app;ies to our observable universe.

so, it's not spacetime being flat, according to that, but the universe.

46. There are two things here, both labled the 'curvature of space', and they are actually two different things.

The first is the local curvature of space, caused by gravitational fields. In this case, it means that space/time varies from a Euclidian geometry, so that the angles of a triangle add up to more than 180 degrees, parallel lines can intersect, and a straight line is not the shortest distance between two points. This is mass curving space.

The other thing referred to as the curvature of space is the overall geometry of the universe, is it closed, open, or flat. This appears to me to be what curious mind is referring to.

47. Originally Posted by AlexG
There are two things here, both labled the 'curvature of space', and they are actually two different things.

The first is the local curvature of space, caused by gravitational fields. In this case, it means that space/time varies from a Euclidian geometry, so that the angles of a triangle add up to more than 180 degrees, parallel lines can intersect, and a straight line is not the shortest distance between two points. This is mass curving space.

The other thing referred to as the curvature of space is the overall geometry of the universe, is it closed, open, or flat. This appears to me to be what curious mind is referring to.
yes, local curvature is easily dedected to not match 180 degrees, which shows as you stated; a straight line is not the shortest distance between 2 points.

umm or a straight line would be the shorter path, but needs more energy.

48. What I don't quite understand is how its possible that two observers in different gravitational fields, subject to different amounts of curvature, can both agree as to which observer is in the stronger field? Or rather which observer is subject to greater curvature?

If my world is curved, but looks straight to me, and your world is straight....... wouldn't your world look curved to me? (Given that my curved world looks straight to me?)

49. Originally Posted by kojax
What I don't quite understand is how its possible that two observers in different gravitational fields, subject to different amounts of curvature, can both agree as to which observer is in the stronger field? Or rather which observer is subject to greater curvature?
The observer in the stronger field will see a blueshift in their observations of the observer in the weaker field. The observer in the weaker field will see a redshift in their observations of the observer in the stronger field.

Originally Posted by kojax
If my world is curved, but looks straight to me, and your world is straight....... wouldn't your world look curved to me? (Given that my curved world looks straight to me?)
An orbit is a straight line through curved space. A measurement of orbital speed and radius will tell you how much curvature there is.

50. I guess that's what I was missing. We can see the curvature of our own region of space. We notice, for example, that the Earth is orbiting the sun. We don't think it's flying along in a straight line.

But it leaves the question: what reference point are we using to determine which way is "straight"? If light is following a bent path to reach us, then a direction that seems straight ahead, could in fact be off to one side or the other. (Or rather, maybe there is no "in fact" about it..... just different perspectives?)

51. But it leaves the question: what reference point are we using to determine which way is "straight"?
Intrinsic curvature can be measured and calculated; a trajectory either has curvature, or it doesn't. We don't need a reference point or direction for that. Remember that curvature is an intrinsic property.

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