# Thread: Question on Warping of Space-Time

1. If space-time near a gravitational object is being warped toward the object, does that imply that it should also be getting warped in an equal and opposite direction somewhere else?

I'm thinking of how a black hole pulls light into it. It basically grabs the area of space where the light is traveling, and pulls the space itself toward the center, right? (That might be oversimplified, and I'd love if someone could expand that explanation)

If space is getting pulled into a black hole, doesn't it have to be expanding somewhere else? At least we know the degree to which something experiences the pull diminishes further out.

2.

3. kojax, the idea of space-time being curved is simply an analogy to explain general relativity easily. Space-time does not actually curve; an object behaves as if it is on a curved surface, but space-time is not the cause. The only thing is that time dilation now occurs at different points in the graviational field.

Please remember that: the curvature of space-time is only a useful analogy. It is not what actually happens.

4. But then, what causes an object at rest near the gravitational body to begin moving toward it?

5. Originally Posted by Liongold
kojax, the idea of space-time being curved is simply an analogy to explain general relativity easily. Space-time does not actually curve; an object behaves as if it is on a curved surface, but space-time is not the cause. The only thing is that time dilation now occurs at different points in the graviational field.

Please remember that: the curvature of space-time is only a useful analogy. It is not what actually happens.
No.

Space-time is most certainly curved.

That is what the general theory of relativity is all about. It describes the curvature tensor that applies to the space-time manifold very precisely as being proportinional to the the stress-energy tensor, which is the source of Wheeler's famous quote that "Matter tells space how to curve and space tells matter how to move".

The curvature of space-time is quite real and it is not merely an analogy. It is in fact a central facet of modern physics.

6. So, does space getting pulled inward toward a gravitational body imply that it must be stretching/expanding somewhere else?

7. No.

Space-time is most certainly curved.

That is what the general theory of relativity is all about. It describes the curvature tensor that applies to the space-time manifold very precisely as being proportinional to the the stress-energy tensor, which is the source of Wheeler's famous quote that "Matter tells space how to curve and space tells matter how to move".

The curvature of space-time is quite real and it is not merely an analogy. It is in fact a central facet of modern physics.
I will have to disagree with you here, DrRocket, although not completely.

If you remember the principle of equivalence, then being in a gravitational field is no different from acceleration. By a simple thought experiment, it is easy to show that an observer in acceleration will observe a different value for pi. In order to make myself clearer, I will describe the exact nature of the thought experiment:

Imagine a circular chamber, in which tow observers are enclosed. The chamber begins to accelerate. Armed with rulers, the observers set out to measure the circumference and diameter respectively. The first observer measures the circumference; because his ruler will contract in the direction of motion, he will measure a larger circumference. The second observer's ruler, however, is perpendicular to the direction of motion, and hence will not contract; obviously, the observer will measure the same diameter as he would at rest.

The chamber stops. The two observers meet, and with their measurements, begin to calculate the value of pi, which will turn out different, because of an observed change in the circumference without a corresponding change in the diameter. However, pi can only change when measured on a curved surface, and from this it is possible to deduce the notion of a curved space-time in a gravitational field.

My bone of contention, if you will, is based on this. Obviously, the principle of equivalence demands that pi be observed to change in a gravitational field too. Yet if a curved space-time operates as a real, physical entity in a gravitational field, surely it should do the same in accelerated motion. However, we do not observe any physical 'curvature' of space or time in accelerated motion; while time dilation and Fitzgerald contraction do occur, I doubt you can label that as the curvature of space and time. You do not measure time to suddenly curve; nor do you observe space do the same.

In the thought experiment I described above, the reason pi came out different was because of a difference in the actual observation of the circumference when it was at rest and at motion. And the principle of equivalence allows us to substitute the notion of a curved space-time with instead a circular chamber, undergoing acceleration. It is obvious from this that we cannot conclude that space-time is an actual physical thing, just as acceleration is not an actual physical thing: both are effects that can be observed and experienced yet cannot be touched and hence have no physical status. If it was, we could not replace this space-time with an accelerating circular chamber as easily as we can.

Since space-time cannot be said to be an actual physical thing, or something we can touch, but only something we can experience, it follows that the notion of its curvature is also only something that can be experienced; in no other way is it physical. While we can experience its effects, this does not automatically mean that it is a physical, tangible thing.

That is why I said that the curvature of space-time is only an analogy, because space-time does not curve in a physical sense. We can experience the effects of such a curvature, but in no way can we conclude that it is actually because such a curvature actually exists, in a physical sense, because we can just as easily replace the notion with an accelerating circular chamber. Mathematically, yes, space-time does curve, and is the reason why general relativity works so well; physically, space-time has no business being curved, or at least we can't see, or feel, or in any way sense them curve, because they are not actual physical things.

Most people, however, conclude that space-time actually curve in a physical sense, instead of mathematically, and this can be the basis of questions like kojax's.

I hope you understand, DrRocket, why I stated that space-time curvature is only a useful analogy to explain general relativity and not actually a physical event. You are not wrong in saying that it is curved, but this is only inb a mathematical sense; physically, we have no way of determining if they are actually curving.

Oh, and kojax: since space-time does not actually curve in a physical sense, it follows that it does not need to expand, again in a physical sense. Mathematically, however, is another question.

8. Originally Posted by Liongold
No.

Space-time is most certainly curved.

That is what the general theory of relativity is all about. It describes the curvature tensor that applies to the space-time manifold very precisely as being proportinional to the the stress-energy tensor, which is the source of Wheeler's famous quote that "Matter tells space how to curve and space tells matter how to move".

The curvature of space-time is quite real and it is not merely an analogy. It is in fact a central facet of modern physics.
I will have to disagree with you here, DrRocket, although not completely.

If you remember the principle of equivalence, then being in a gravitational field is no different from acceleration. By a simple thought experiment, it is easy to show that an observer in acceleration will observe a different value for pi. In order to make myself clearer, I will describe the exact nature of the thought experiment:

Imagine a circular chamber, in which tow observers are enclosed. The chamber begins to accelerate. Armed with rulers, the observers set out to measure the circumference and diameter respectively. The first observer measures the circumference; because his ruler will contract in the direction of motion, he will measure a larger circumference. The second observer's ruler, however, is perpendicular to the direction of motion, and hence will not contract; obviously, the observer will measure the same diameter as he would at rest.

The chamber stops. The two observers meet, and with their measurements, begin to calculate the value of pi, which will turn out different, because of an observed change in the circumference without a corresponding change in the diameter. However, pi can only change when measured on a curved surface, and from this it is possible to deduce the notion of a curved space-time in a gravitational field.

My bone of contention, if you will, is based on this. Obviously, the principle of equivalence demands that pi be observed to change in a gravitational field too. Yet if a curved space-time operates as a real, physical entity in a gravitational field, surely it should do the same in accelerated motion. However, we do not observe any physical 'curvature' of space or time in accelerated motion; while time dilation and Fitzgerald contraction do occur, I doubt you can label that as the curvature of space and time. You do not measure time to suddenly curve; nor do you observe space do the same.

In the thought experiment I described above, the reason pi came out different was because of a difference in the actual observation of the circumference when it was at rest and at motion. And the principle of equivalence allows us to substitute the notion of a curved space-time with instead a circular chamber, undergoing acceleration. It is obvious from this that we cannot conclude that space-time is an actual physical thing, just as acceleration is not an actual physical thing: both are effects that can be observed and experienced yet cannot be touched and hence have no physical status. If it was, we could not replace this space-time with an accelerating circular chamber as easily as we can.

Since space-time cannot be said to be an actual physical thing, or something we can touch, but only something we can experience, it follows that the notion of its curvature is also only something that can be experienced; in no other way is it physical. While we can experience its effects, this does not automatically mean that it is a physical, tangible thing.

That is why I said that the curvature of space-time is only an analogy, because space-time does not curve in a physical sense. We can experience the effects of such a curvature, but in no way can we conclude that it is actually because such a curvature actually exists, in a physical sense, because we can just as easily replace the notion with an accelerating circular chamber. Mathematically, yes, space-time does curve, and is the reason why general relativity works so well; physically, space-time has no business being curved, or at least we can't see, or feel, or in any way sense them curve, because they are not actual physical things.

Most people, however, conclude that space-time actually curve in a physical sense, instead of mathematically, and this can be the basis of questions like kojax's.

I hope you understand, DrRocket, why I stated that space-time curvature is only a useful analogy to explain general relativity and not actually a physical event. You are not wrong in saying that it is curved, but this is only inb a mathematical sense; physically, we have no way of determining if they are actually curving.

Oh, and kojax: since space-time does not actually curve in a physical sense, it follows that it does not need to expand, again in a physical sense. Mathematically, however, is another question.
What in the world do you think you are talking about ? This is complete gibberish.

I think you need to go read something on the subject of differential geometry and either Riemannian or (preferably) pseudo-Riemannian manifolds.

9. Originally Posted by DrRocket
What in the world do you think you are talking about ? This is complete gibberish.

I think you need to go read something on the subject of differential geometry and either Riemannian or (preferably) pseudo-Riemannian manifolds.
It made complete sense to me DrRocket. Not sure if I buy the argument or not, since common sense and logic seem to break down pretty easily when you're talking about relativity, but the reasoning made sense to me.

10. kojax, as far as I know, 'space' doesn't move at all,

Space is a lack of matter and therefore is unaffected by properties of Matter such as gravity,

Black holes simply pull in all matter within their Event Horizon, if you imagine all of Matter like magnets, they all pull on all matter around them and are equally pulled by the matter around them, Black holes are simply very powerful, small magnets and as they pull in the other magnets the combined force of so many magnets pulls things in from futher away faster

However since we no next to nothing about the universe it's entirely possible Space is in fact some form of unidentified mass that is pulled into a black hole,
in this instance space would be equally distorted at the end of space as it's pulled into a black hole if space had an end! even though it's nearly impossible to imagine, (seriously just try to picture an endless universe) as far as we can tell space has no end, it doesn't curve into a sphere, it just goes on....
the reasoning behind this is that space is a false vacuum if the universe was finite and Space was just that then the universe would be a vacuum and everything would be torn apart and scattered equally throughout the universe. as is evident by our continued 'non-scattering' the universe is not a vaccum, it just has some of the properties of a vacuum (like insanely low pressure causing people to explode like on tv)
now the only two reasons for this is either, Space is not really nothing, or the Universe is endless, and since we have proven to the extent of our knowledge that Space is indeed nothing, the latter must be true

11. Originally Posted by Liongold
... In order to make myself clearer, I will describe the exact nature of the thought experiment:

Imagine a circular chamber, in which tow observers are enclosed. The chamber begins to accelerate. Armed with rulers, the observers set out to measure the circumference and diameter respectively. The first observer measures the circumference; because his ruler will contract in the direction of motion, he will measure a larger circumference. The second observer's ruler, however, is perpendicular to the direction of motion, and hence will not contract; obviously, the observer will measure the same diameter as he would at rest.
This is an amazingly sweet thought experiment, however there's one small issue.

The guy measuring the circumference's ruler is shorter, and the circumference is shorter - both. So he measures it to be the same length as it would be if it were at rest.

But... relativity seems to enter into one of its great contradictions. How can the circumference shrink and the diameter remain the same?

Apparently, if you made 2 marks on the outer wall of the chamber before it was accelerated, and measured how far apart the marks were, and then stood at the center of the room with a protractor and measured the angle between the two marks, - all prior to accelerating the room. Then accelerated the room, and then stood at the center and used the protractor again, relativity seems to tell us that the angle would be a smaller angle on the second measurement.

But that soooo totally contradicts, because no part of the wall seems to be getting longer. All parts just seem to be getting shorter. If you made marks all the way around prior to accelerating, then prior to accelerating, the angles would add up to 360 degrees.

After accelerating would the angles still add up to 360 degrees?

My bone of contention, if you will, is based on this. Obviously, the principle of equivalence demands that pi be observed to change in a gravitational field too. Yet if a curved space-time operates as a real, physical entity in a gravitational field, surely it should do the same in accelerated motion. However, we do not observe any physical 'curvature' of space or time in accelerated motion; while time dilation and Fitzgerald contraction do occur, I doubt you can label that as the curvature of space and time. You do not measure time to suddenly curve; nor do you observe space do the same.
I guess space time can't be just getting pulled in toward the center, exactly, like some grand conveyor belt, because then it wouldn't be accelerating, only moving. And,... it's clear that objects accelerate.

I may have to change how I visualize this. But I have to still be able to grasp how it is that black holes can drag in light toward them, when we know light doesn't accelerate or decelerate (at least not in the direction of motion).

Since space-time cannot be said to be an actual physical thing, or something we can touch, but only something we can experience, it follows that the notion of its curvature is also only something that can be experienced; in no other way is it physical. While we can experience its effects, this does not automatically mean that it is a physical, tangible thing.
It depends what you consider tangible. It can probably still be visualized, just not using a simple 3d model. That 4th dimension is a really crazy one. To say it's curved is probably accurate, but it's very hard to visualize in 4D.

12. The guy measuring the circumference's ruler is shorter, and the circumference is shorter - both. So he measures it to be the same length as it would be if it were at rest.
While the guy would be observed to be shorter from another's point of view, from his own point of view, he would still be the same length. For him, the ruler will appear to have shrunk relative to him. Also, the circumference won't be shorter; it won't shrink, as you seem to think, although it will appear to from the point of view of someone outside the chamber. However, the observers inside the chamber will measure it to be longer, since they are in contact and technically part of the chamber, in essence 'balancing' the outside observers's measurement.

But that soooo totally contradicts, because no part of the wall seems to be getting longer. All parts just seem to be getting shorter. If you made marks all the way around prior to accelerating, then prior to accelerating, the angles would add up to 360 degrees.

After accelerating would the angles still add up to 360 degrees?
Why would they have to add up to 360 degrees? Don't forget, the surface of a circular chamber is a curved surface, so different rules apply.

But... relativity seems to enter into one of its great contradictions. How can the circumference shrink and the diameter remain the same?
No, no; they will be observed to shrink, rather than actually shrink. They are still the same, but from the point of view of the observers', they are different. If you were part of the circumference, you would still measure the same length of the circumference.

I may have to change how I visualize this. But I have to still be able to grasp how it is that black holes can drag in light toward them, when we know light doesn't accelerate or decelerate (at least not in the direction of motion).
In an accelerating spaceship, for example, light will be observed to 'bend'. Because of the principle of equivalence, the same phenomenon will be observed in a gravitational field. Simply consider a black hole's gravitational field to be equivalent to a ship undergoing extraordinary acceleration.

13. Originally Posted by Liongold
It is obvious from this that we cannot conclude that space-time is an actual physical thing, just as acceleration is not an actual physical thing: both are effects that can be observed and experienced yet cannot be touched and hence have no physical status.
Well, aside from the fact that I don't quite understand the difference between a "physical thing" and an "actual physical thing", let me ask you this:

If, as you say above, that "both are effects that can be observed and experienced", what more do you require for something to be real? You seem to imply that touching is all that makes it real, which is plainly wrong.

Mathematically, yes, space-time does curve,
Oooo, good old Einstein - got something right, at least
physically, space-time has no business being curved,
So you're telling spacetime its business? You're telling the natural laws what they should be, rather than letting them tell you? This ain't science.

14. Originally Posted by Liongold
The guy measuring the circumference's ruler is shorter, and the circumference is shorter - both. So he measures it to be the same length as it would be if it were at rest.
While the guy would be observed to be shorter from another's point of view, from his own point of view, he would still be the same length. For him, the ruler will appear to have shrunk relative to him. Also, the circumference won't be shorter; it won't shrink, as you seem to think, although it will appear to from the point of view of someone outside the chamber. However, the observers inside the chamber will measure it to be longer, since they are in contact and technically part of the chamber, in essence 'balancing' the outside observers's measurement.
I'm not sure that's how Lorentz contraction works. I'm pretty sure the observer standing near the outer wall of this chamber and facing in the direction of motion, (Ie, if the chamber is spinning clockwise, then he's positioned so the wall is on his left, and he's facing forward) , will observe *all* distances in that direction to be shorter.

That's why passengers on a space ship headed toward Proxima Centauri at relativistic speeds, would observe themselves to arrive sooner than 4 years. (It's 4 light years away). From their perspective, the distance itself is shorter, so it's no contradiction to be arriving sooner.

But that soooo totally contradicts, because no part of the wall seems to be getting longer. All parts just seem to be getting shorter. If you made marks all the way around prior to accelerating, then prior to accelerating, the angles would add up to 360 degrees.

After accelerating would the angles still add up to 360 degrees?
Why would they have to add up to 360 degrees? Don't forget, the surface of a circular chamber is a curved surface, so different rules apply.
Because the curved wall of the chamber occupies all 360 degrees of the observers view. If the marks are made at regular intervals all the way around, the measured angles between them *should* add up to 360 degrees. But relativity seems to predict that they won't.

That's the beauty of your experiment. Even though the walls are moving at a relativistic speed, the observer standing in the middle of the room may not be moving very fast at all, in any direction. (Assuming we allow it to be a very, very large chamber.)

But... relativity seems to enter into one of its great contradictions. How can the circumference shrink and the diameter remain the same?
No, no; they will be observed to shrink, rather than actually shrink. They are still the same, but from the point of view of the observers', they are different. If you were part of the circumference, you would still measure the same length of the circumference.
While we, the thought experimenters, may view the room as a single object, I'm pretty sure the universe does not. Each atom that makes up that wall is a separate entity unto itself. Each atom perceives itself to be moving at a relativistic speed in a straight line,( tangient to the curvature of the wall.)

I may have to change how I visualize this. But I have to still be able to grasp how it is that black holes can drag in light toward them, when we know light doesn't accelerate or decelerate (at least not in the direction of motion).
In an accelerating spaceship, for example, light will be observed to 'bend'. Because of the principle of equivalence, the same phenomenon will be observed in a gravitational field. Simply consider a black hole's gravitational field to be equivalent to a ship undergoing extraordinary acceleration.
That leads to my perception that space itself is being dragged toward you, doesn't it? Except.... it's coming at you in an accelerated fashion, rather than a constant speed, which is hard to account for....

15. Well, aside from the fact that I don't quite understand the difference between a "physical thing" and an "actual physical thing", let me ask you this:

If, as you say above, that "both are effects that can be observed and experienced", what more do you require for something to be real? You seem to imply that touching is all that makes it real, which is plainly wrong.
Okay, perhaps a little clarification is in order: I simply put the 'actual' there for emphasis. There is no distinction between a physicla and an actual physical thing.

Secondly, the question of reality is a tricky one. I am simply trying to state that for something to be physically 'real', it has to have a physical existence, defined by a certain parameter or condition. I took this condition to be a material existence i.e something we can feel, see, hear, taste and/or smell. Features like velocity or acceleration are not physical things because they are not material; they exist, certainly, but not as physical things, because they do not satisfy the conditions necessary for physical existence. They exist, yes, but instead as 'mathematical' concepts, in that they can be measured qualitatively and have a rigidly defined existence. But perhaps you might have a different condition?

This is starting to seem like it is diverging into philosophy...

So you're telling spacetime its business? You're telling the natural laws what they should be, rather than letting them tell you? This ain't science.
No, I'm simply saying that there's a difference between space-time physically curving and mathematically curving. Space-time does not physically curve; it does curve mathematically. I've given my reasons in a previous post in this thread, so unless you would like me to reiterate them again, I think I've already explained why this is so.

Why on earth would I try to dictate natural laws? It's a common assumption that space-time literally curves, when it really doesn't: both space and time are, for want of a better word, subjective. Both depend on the observer, and time, for one, is extremely hard to even define. To say that both have an objective existence is just plain wrong. That's all I'm trying to point out.

16. I'm not sure that's how Lorentz contraction works. I'm pretty sure the observer standing near the outer wall of this chamber and facing in the direction of motion, (Ie, if the chamber is spinning clockwise, then he's positioned so the wall is on his left, and he's facing forward) , will observe *all* distances in that direction to be shorter.

That's why passengers on a space ship headed toward Proxima Centauri at relativistic speeds, would observe themselves to arrive sooner than 4 years. (It's 4 light years away). From their perspective, the distance itself is shorter, so it's no contradiction to be arriving sooner.
It's an indication of just how long it's been since I've last read anything on Lorentz contraction that I can't even think of how to answer you correctly without thinking I'm wrong in some small, essential point. Nevertheless, I'll try to answer this. If anyone notes any mistakes, I would be most grateful if they could tell me.

Well, the observer can be said to be moving relative to the ruler, yes? So, for him, it is the ruler that will contract, while from the ruler's perspective, the observer is the one who's contracting. And since the only way the observer can objectively measure the circumference is with the ruler, he must accept that the ruler is giving him a different circumference than when they are at rest. Note that here it is not so much the circumference that is getting longer; it is just that both the observer and the ruler are now shorter than before. And naturally there will have to be a different measurement of distance than before.

And if I might, there seems to be something wrong with the Proxima Centauri thought experiment. Why would the distance seem shorter? If they are moving at extremely large speeds, then time dilation will occur and time will seem longer. To balance this, a longer distance will be needed. So the observers will, in fact, observe a different and longer distance than when they were at rest.

Because the curved wall of the chamber occupies all 360 degrees of the observers view. If the marks are made at regular intervals all the way around, the measured angles between them *should* add up to 360 degrees. But relativity seems to predict that they won't.

That's the beauty of your experiment. Even though the walls are moving at a relativistic speed, the observer standing in the middle of the room may not be moving very fast at all, in any direction. (Assuming we allow it to be a very, very large chamber.)
You're right, they won't. There has to be some contraction because of the motion, so the angles should not add up to 360 degrees.

And, technically, it's not my thought experiment; Brian Greene described it in his book, The Elegant Universe, and I took it from there.

While we, the thought experimenters, may view the room as a single object, I'm pretty sure the universe does not. Each atom that makes up that wall is a separate entity unto itself. Each atom perceives itself to be moving at a relativistic speed in a straight line,( tangient to the curvature of the wall.)
Yes, but we're not concerned about the atoms in the experiment, are we? True, the effect you describe is a very striking and elegant picture; yet here we are dealing with only three objects: the two observers and the chamber. The atoms aren't supposed to interfere, since they are all part of the wall. And since they are all part of the wall, it is far simpler to deal with the whole wall rather than all the atyoms of the wall.

That leads to my perception that space itself is being dragged toward you, doesn't it? Except.... it's coming at you in an accelerated fashion, rather than a constant speed, which is hard to account for....
I don't quite think it does lead to your perception. It's not that space is being dragged to you; it's that you're being dragged in by a gravitational field, which is exactly equal to you undergoing a certain amount of acceleration.

17. Originally Posted by Liongold

Well, the observer can be said to be moving relative to the ruler, yes? So, for him, it is the ruler that will contract, while from the ruler's perspective, the observer is the one who's contracting. And since the only way the observer can objectively measure the circumference is with the ruler, he must accept that the ruler is giving him a different circumference than when they are at rest. Note that here it is not so much the circumference that is getting longer; it is just that both the observer and the ruler are now shorter than before. And naturally there will have to be a different measurement of distance than before.
From what I can tell, relativity falls apart if you allow the observer to make corrections for relativity in the process of observing relativity.

He knows his ruler is getting shorter (because he's probably a scientist), but he's not supposed to know that. He's supposed to think his ruler stayed the same size, because looking at in his hand right now, it looks like it's the same size. The wall near him also looks like it hasn't gotten any shorter.

And if I might, there seems to be something wrong with the Proxima Centauri thought experiment. Why would the distance seem shorter? If they are moving at extremely large speeds, then time dilation will occur and time will seem longer. To balance this, a longer distance will be needed. So the observers will, in fact, observe a different and longer distance than when they were at rest.
The time dilation is what makes the trip appear to take less than 4 years. So, without Lorentz contraction to make the distance appear shorter, the passengers would observe themselves to have traveled 4 light years in less than 4 years.

Because the curved wall of the chamber occupies all 360 degrees of the observers view. If the marks are made at regular intervals all the way around, the measured angles between them *should* add up to 360 degrees. But relativity seems to predict that they won't.

That's the beauty of your experiment. Even though the walls are moving at a relativistic speed, the observer standing in the middle of the room may not be moving very fast at all, in any direction. (Assuming we allow it to be a very, very large chamber.)
You're right, they won't. There has to be some contraction because of the motion, so the angles should not add up to 360 degrees.

And, technically, it's not my thought experiment; Brian Greene described it in his book, The Elegant Universe, and I took it from there.
Wow. Now I'm all curious what Brian Greene concluded, so I may have to go get the book and read it.

This is the part that's so weird. A wall that occupies all 360 degrees of the observer's field of vision, but when he measures the angles, they don't add up to 360 degrees? I wonder how that looks.

On the other hand, maybe it all fits together once we account for the acceleration from centripetal force. Do you think the acceleration cancels the effect? (I'm really bad at trying to apply acceleration to Relativity).

18. From what I can tell, relativity falls apart if you allow the observer to make corrections for relativity in the process of observing relativity.

He knows his ruler is getting shorter (because he's probably a scientist), but he's not supposed to know that. He's supposed to think his ruler stayed the same size, because looking at in his hand right now, it looks like it's the same size. The wall near him also looks like it hasn't gotten any shorter.
Well, as far as I can see, no contradiction emerges if you allow the observed distance to vary. Certainly, one can say that since Lorentz-Fitzgerald contraction is required, it makes sense that an observer should measure a longer distance. For example, the crew of the spaceship going to Proxima Centauri must conclude that relativity requires that their spaceship contracts, and so won't be surprised to note tha the distance appears longer, because if you cross the same distance while steadily becoming smaller, the journey will seem longer.

Also, another argument is that the observers that since time slows down at relativistic speeds, in order to get the same speed for their rocket, they must measure the distance to be longer too.

See it for yourself. If a rocket moving at a speed close to c, which we denote as v, time dilation occurs; we denote the time measured by an observer at rest relative to the rocket as t, and the time measured by the crew of the rocket will be t'. The distance to Proxima Centauri we write as equal to D.

Obviously, the speed is measured by

from the point of somone at rest.

It follows that the observers must measure the same speed, because if it wasn't, they would feel accelerational effects; however, the time dilation issue poses a problem. The only way to solve this will be to observe another distance, which we call D'.

Therefore,

Which is why the observers are not permitted to measure the same distance. If they did, they would have to feel acceleration, which is impossible.

Returning to the chamber thought experiment, why should he think it is the same size? He's moving relative to it, if you remember, so he has to measure Lorentz contraction for it. Naturally, the ruler will appear shorter.

The time dilation is what makes the trip appear to take less than 4 years. So, without Lorentz contraction to make the distance appear shorter, the passengers would observe themselves to have traveled 4 light years in less than 4 years.
The Lorentz contraction would make the distance appear longer, not shorter. I've already given you the reason why in this post.

Wow. Now I'm all curious what Brian Greene concluded, so I may have to go get the book and read it.
Given it's meant to popularise string theory, all Brian Greene did was to provide aid in understanding general relativity so that readers could understand other parts of the book. This thought experiment was the way he choose to enlighten the reader as to how Einstein concluded that space-time was 'curved'.

This is the part that's so weird. A wall that occupies all 360 degrees of the observer's field of vision, but when he measures the angles, they don't add up to 360 degrees? I wonder how that looks.

On the other hand, maybe it all fits together once we account for the acceleration from centripetal force. Do you think the acceleration cancels the effect? (I'm really bad at trying to apply acceleration to Relativity).
Actually, kojax, there is no reason why the effect should be canceled out. Indeed, all the effect points out is that something is in motion, and nothing else. What is moving is impossible to conclude, thanks to the principle of relativity. There really is no reason for it to vanish.

And I highly doubt the acceleration will cancel it out, given that it's the acceleration causing it in the first place.

19. Originally Posted by Liongold
Well, as far as I can see, no contradiction emerges if you allow the observed distance to vary. Certainly, one can say that since Lorentz-Fitzgerald contraction is required, it makes sense that an observer should measure a longer distance. For example, the crew of the spaceship going to Proxima Centauri must conclude that relativity requires that their spaceship contracts, and so won't be surprised to note tha the distance appears longer, because if you cross the same distance while steadily becoming smaller, the journey will seem longer.
The real distance between you and Proxima is shorter that 4 light years, in your inertial perspective. This is once you're done accelerating, and are now just coasting.

Also, another argument is that the observers that since time slows down at relativistic speeds, in order to get the same speed for their rocket, they must measure the distance to be longer too.

See it for yourself. If a rocket moving at a speed close to c, which we denote as v, time dilation occurs; we denote the time measured by an observer at rest relative to the rocket as t, and the time measured by the crew of the rocket will be t'. The distance to Proxima Centauri we write as equal to D.

Obviously, the speed is measured by

from the point of somone at rest.
That means that, if t diminishes, velocity increases. To a person experiencing time dilation, everything else seems to be going really fast. I mean, if you took a drug that slowed your metabolism, the world would seem to be blowing by you like a whirlwind. In contrast, if you take something that accelerates your metabolism, the world seems slower.

It follows that the observers must measure the same speed, because if it wasn't, they would feel accelerational effects; however, the time dilation issue poses a problem. The only way to solve this will be to observe another distance, which we call D'.

Therefore,

Which is why the observers are not permitted to measure the same distance. If they did, they would have to feel acceleration, which is impossible.
In the space ship example, the distance between them and Proxima only shrunk during the acceleration stage of reaching their fraction of C. Once they stopped accelerating the distance stopped shrinking, however it will stay small for the rest of the trip.

All other distances forward and backward in that same direction appear to have shrunk as well.

Returning to the chamber thought experiment, why should he think it is the same size? He's moving relative to it, if you remember, so he has to measure Lorentz contraction for it. Naturally, the ruler will appear shorter.

The time dilation is what makes the trip appear to take less than 4 years. So, without Lorentz contraction to make the distance appear shorter, the passengers would observe themselves to have traveled 4 light years in less than 4 years.
The Lorentz contraction would make the distance appear longer, not shorter. I've already given you the reason why in this post.
What Lorentz contraction does is allow that both d and t are shrinking, so your apparent velocity D/t doesn't exceed C. Time dilation makes you seem to go faster, Lorentz contraction makes you seem to go slower. They balance so that all velocities appear smaller than C.

If t shrinks, but d grows, then your apparent speed would be exponentially faster. If both shrink, your speed doesn't grow at all.

This is the part that's so weird. A wall that occupies all 360 degrees of the observer's field of vision, but when he measures the angles, they don't add up to 360 degrees? I wonder how that looks.

On the other hand, maybe it all fits together once we account for the acceleration from centripetal force. Do you think the acceleration cancels the effect? (I'm really bad at trying to apply acceleration to Relativity).
Actually, kojax, there is no reason why the effect should be canceled out. Indeed, all the effect points out is that something is in motion, and nothing else. What is moving is impossible to conclude, thanks to the principle of relativity. There really is no reason for it to vanish.

And I highly doubt the acceleration will cancel it out, given that it's the acceleration causing it in the first place.
No, the velocity is what's causing the contraction. If not for an acceleration (acting opposite of centripetal force), all the particles that make up that wall would break apart and fly away in straight lines tangient to the curvature of the wall.

Their velocity is what is making the distances along the wall shorter. But strangely it isn't making the radius of the room any smaller. It's such a contradiction. The radius of the circle remains the same, but the circumference shrinks?

I'm thinking one of 3 possibilities:

1) - The acceleration required to keep the particles in the wall from leaving, counters the effect? (Which I suggest out of ignorance, because I don't really understand how acceleration affects relativity very well)

2) - The guy standing in the middle of the room observes the wall to be an elipse no matter which way he faces, and the particular section he's looking at, at any given moment, appears to be the long (or short, I'm not sure which) part of that elipse.

I don't know why #2 would happen, though. If the room is big enough, then the observer standing in the middle of it with his protractor is moving at only a very small speed. He shouldn't be suffering any effects of relativity at all, just observing them to happen in the walls.

3) - ... Maybe Lorentz contraction is only a perceived effect. If you were sitting half way between Earth and Proxima Centauri, at rest, as a space ship passed you on its way to Proxima, and that space ship is going say.... 3/4 C ... Would the space ship look shorter to you?

(I'm assuming that your positioned far enough in direction perpendicular to the space ship's motion that you can get a good look at it as is passes you)

20. The real distance between you and Proxima is shorter that 4 light years, in your inertial perspective. This is once you're done accelerating, and are now just coasting.
True, but here we're considering the distance between you at rest and Proxima Centauri.

That means that, if t diminishes, velocity increases. To a person experiencing time dilation, everything else seems to be going really fast. I mean, if you took a drug that slowed your metabolism, the world would seem to be blowing by you like a whirlwind. In contrast, if you take something that accelerates your metabolism, the world seems slower.
Actually, it won't. T doesn't diminish in that formula, time dilation means that it grows, because one second at rest means to you, at a certain velocity, 1.5 seconds. Likewise, one second at rest means, at c, infinity; a clear indication that the value of t grows in time dilaiton, rather than diminish.

This might seem a bit confusing, but it's actually quite clear. Time dilation means that time slows down, so that one second at rest means to someone moving at v 1.5 or 2 seconds. You can directly infer that if time slows down, the value of t from the perspective of someone in motion grows.

So, to correct you, for someone going really fast, everything else seems to be going even more slowly. If you blew by at c, suffice it to say that it will appear to you as if nothing is moving at all, because time has slowed down so much that to you, one second at rest is equal to an infinity of seconds at c.

In the space ship example, the distance between them and Proxima only shrunk during the acceleration stage of reaching their fraction of C. Once they stopped accelerating the distance stopped shrinking, however it will stay small for the rest of the trip.

All other distances forward and backward in that same direction appear to have shrunk as well.
Now we're taking the analogy too far. While it is true that the distance will appear to have shrunk when accelerating, the distance will always shrink no matter what speed you're travelling at in motion, because you're covering it as we speak. What happens here is that they will think that the distance seems longer than it should. That is all there is to it.

What Lorentz contraction does is allow that both d and t are shrinking, so your apparent velocity D/t doesn't exceed C. Time dilation makes you seem to go faster, Lorentz contraction makes you seem to go slower. They balance so that all velocities appear smaller than C.

If t shrinks, but d grows, then your apparent speed would be exponentially faster. If both shrink, your speed doesn't grow at all.
What Lorentz contraction does is cancel out the growth of the value of t by a corresponding growth in the value of D. I've already explained that if time slows down, then that is equivalent to the value of t growing, rather than diminishing. Consequently, Lorentz contraction enables you to consider the possibility that D has grown longer.

No, the velocity is what's causing the contraction. If not for an acceleration (acting opposite of centripetal force), all the particles that make up that wall would break apart and fly away in straight lines tangient to the curvature of the wall.

Their velocity is what is making the distances along the wall shorter. But strangely it isn't making the radius of the room any smaller. It's such a contradiction. The radius of the circle remains the same, but the circumference shrinks?

I'm thinking one of 3 possibilities:

1) - The acceleration required to keep the particles in the wall from leaving, counters the effect? (Which I suggest out of ignorance, because I don't really understand how acceleration affects relativity very well)

2) - The guy standing in the middle of the room observes the wall to be an elipse no matter which way he faces, and the particular section he's looking at, at any given moment, appears to be the long (or short, I'm not sure which) part of that elipse.

I don't know why #2 would happen, though. If the room is big enough, then the observer standing in the middle of it with his protractor is moving at only a very small speed. He shouldn't be suffering any effects of relativity at all, just observing them to happen in the walls.

3) - ... Maybe Lorentz contraction is only a perceived effect. If you were sitting half way between Earth and Proxima Centauri, at rest, as a space ship passed you on its way to Proxima, and that space ship is going say.... 3/4 C ... Would the space ship look shorter to you?

(I'm assuming that your positioned far enough in direction perpendicular to the space ship's motion that you can get a good look at it as is passes you)
If you look at the thought experiment, it very clearly states that the chamber is accelerating, rather than moving at a constant velocity. Hence, it is the acceleration that is causing the contraction, rather than a constant velocity, as is the case of special relativity.

Their velocity is what is making the distances along the wall shorter. But strangely it isn't making the radius of the room any smaller. It's such a contradiction. The radius of the circle remains the same, but the circumference shrinks?
Why should it be a contradiction? The angle plays a role too, after all, as anybody who knows vectors can tell you. If you cover distance while moving perpendicular to a force applied, no work is said to be done by the force. Likewise, no contraction effect will be noted by the radius because it is perpendicular to the direction of motion. I was surprised too, but it does make sense.

And technically, it is the velocity of the wall here that matters and not the velocity of the atoms, because they are all moving together, with very slight irregularities.

I'm thinking one of 3 possibilities:

1) - The acceleration required to keep the particles in the wall from leaving, counters the effect? (Which I suggest out of ignorance, because I don't really understand how acceleration affects relativity very well)

2) - The guy standing in the middle of the room observes the wall to be an elipse no matter which way he faces, and the particular section he's looking at, at any given moment, appears to be the long (or short, I'm not sure which) part of that elipse.

I don't know why #2 would happen, though. If the room is big enough, then the observer standing in the middle of it with his protractor is moving at only a very small speed. He shouldn't be suffering any effects of relativity at all, just observing them to happen in the walls.

3) - ... Maybe Lorentz contraction is only a perceived effect. If you were sitting half way between Earth and Proxima Centauri, at rest, as a space ship passed you on its way to Proxima, and that space ship is going say.... 3/4 C ... Would the space ship look shorter to you?

(I'm assuming that your positioned far enough in direction perpendicular to the space ship's motion that you can get a good look at it as is passes you)
Your first possibility is a good one, but need not be contemplated; mere acceleration cannot cause atoms to break apart from each other, thanks due to the electrostatic forces between them.

Your second possibility is a bit odd. Why an ellipse? That would mean the circumference is moving inwards at places and outwards at others, which really makes no sense, and isn't even required. What is required is a longer circumference, and it doesn't quite matter how it looks like; what is important is that it is measured to be longer.

If you really wish to imagine what it appears to be, I wish you good luck.

As to your third possibility, that is precisely what Lorentz contraction is. It is a perceived effect in the sense that something is perceived to be shorter at at a certain speed, even though it measures the same when you measure it from the inside. You perceive something to be longer or wshorter, though it really has not changed at all. That was a good example you gave, and, yes, it will look shorter to you. To the people inside it, it will appear to be exactly the same length as it was when at rest.

21. [quote="Liongold"]
Actually, it won't. T doesn't diminish in that formula, time dilation means that it grows, because one second at rest means to you, at a certain velocity, 1.5 seconds. Likewise, one second at rest means, at c, infinity; a clear indication that the value of t grows in time dilaiton, rather than diminish.

This might seem a bit confusing, but it's actually quite clear. Time dilation means that time slows down, so that one second at rest means to someone moving at v 1.5 or 2 seconds. You can directly infer that if time slows down, the value of t from the perspective of someone in motion grows.
You got that completely backwards.

The formula is

where T is the time that passes for our observer "at rest" and t is the time that passes for the "moving" observer. So when v = 0.866c , one second for our "moving" observer equal 2 sec for our observer "at rest".

22. Originally Posted by Liongold
Actually, it won't. T doesn't diminish in that formula, time dilation means that it grows, because one second at rest means to you, at a certain velocity, 1.5 seconds. Likewise, one second at rest means, at c, infinity; a clear indication that the value of t grows in time dilaiton, rather than diminish.

This might seem a bit confusing, but it's actually quite clear. Time dilation means that time slows down, so that one second at rest means to someone moving at v 1.5 or 2 seconds. You can directly infer that if time slows down, the value of t from the perspective of someone in motion grows.

So, to correct you, for someone going really fast, everything else seems to be going even more slowly. If you blew by at c, suffice it to say that it will appear to you as if nothing is moving at all, because time has slowed down so much that to you, one second at rest is equal to an infinity of seconds at c.
This is really easy to get backwards. If I age 1 year, in an amount of time while you age 10 years.... my eyes will have only seen one year worth of motion.

If we're watching the same tree (from a good distance away), and we both watch it over what you perceive as 10 years.. And the tree were to grow a foot per year (I don' t know what kind of tree does that)... We both see it reach 10 feet.

However: I think it took 1 year to grow 10 feet. You think it took 10 years.

The same analogy would hold for ordinary motion. If you perceive that a car took 20 seconds to cross an area of road, I would perceive that it took 2 seconds to cross the same distance.

In the space ship example, the distance between them and Proxima only shrunk during the acceleration stage of reaching their fraction of C. Once they stopped accelerating the distance stopped shrinking, however it will stay small for the rest of the trip.

All other distances forward and backward in that same direction appear to have shrunk as well.
Now we're taking the analogy too far. While it is true that the distance will appear to have shrunk when accelerating, the distance will always shrink no matter what speed you're travelling at in motion, because you're covering it as we speak. What happens here is that they will think that the distance seems longer than it should. That is all there is to it.
What I mean is that, if you finished accelerating by the time you reach Pluto, and you look at Proxima from your space ship, it looks much closer than 4 light years, even though it's still nearly 4 light years away from Earth's perspective.

You could use triangulation. Maybe your space ship is 10 miles wide, so you send observers to the far edges, and they determine the angle toward Proxima Centauri using super precise telescopes, and then crunch some numbers to determine how far away it is. They'll give you an answer substantially lower than 4 light years.

If you look at the thought experiment, it very clearly states that the chamber is accelerating, rather than moving at a constant velocity. Hence, it is the acceleration that is causing the contraction, rather than a constant velocity, as is the case of special relativity.

Good point. So, he's talking about accelerated motion, and I'm thinking of inertial motion. The thought experiment I'm thinking of is different then, but still intriguing.

It makes a big difference for the chamber to be accelerating instead of just coasting along under its own inertia. If it's under its own inertia, then we can totally predict how much the wall will have contracted, but acceleration is much more complicated in GR, it seems.

23. You got that completely backwards.

The formula is

where T is the time that passes for our observer "at rest" and t is the time that passes for the "moving" observer. So when v = 0.866c , one second for our "moving" observer equal 2 sec for our observer "at rest".
Janus, I'm usually not one to disagree with you, but are you sure you've got the formula right? As I recall, it should be:

t' = T / sqrt. 1 - v^2/c^2

where t' is the time that passes for the observer in motion and T is the time that passes for an observer at rest, and not the other way around.

From this formula, it is easy to deduce that since the denominator decreases, the result will be a larger value of t for the observer in motion.

Wikipedia, at least, seems to agree that the formula is the way I have just stated it to be:

http://en.wikipedia.org/wiki/Time_dilation

24. This is really easy to get backwards. If I age 1 year, in an amount of time while you age 10 years.... my eyes will have only seen one year worth of motion.

If we're watching the same tree (from a good distance away), and we both watch it over what you perceive as 10 years.. And the tree were to grow a foot per year (I don' t know what kind of tree does that)... We both see it reach 10 feet.

However: I think it took 1 year to grow 10 feet. You think it took 10 years.

The same analogy would hold for ordinary motion. If you perceive that a car took 20 seconds to cross an area of road, I would perceive that it took 2 seconds to cross the same distance.

What I mean is that, if you finished accelerating by the time you reach Pluto, and you look at Proxima from your space ship, it looks much closer than 4 light years, even though it's still nearly 4 light years away from Earth's perspective.
Correct. But the distance will still seem longer to the people in motion, even though it is shorter than before, as you say.

Good point. So, he's talking about accelerated motion, and I'm thinking of inertial motion. The thought experiment I'm thinking of is different then, but still intriguing.

It makes a big difference for the chamber to be accelerating instead of just coasting along under its own inertia. If it's under its own inertia, then we can totally predict how much the wall will have contracted, but acceleration is much more complicated in GR, it seems.
That it is. :wink:

25. Why say that space bends if it doesn't? Isn't there a better way to put that if it's just mathematical. In Brian Greens Book the fabric of the cosmos he brings up the debate of whether or not space is a "something" or not by using the thought experiment of the spinning bucket. If there was a bucket of water alone in space and was spinning would the water take on a concave shape? I think the conclusion was that it would, I'll have to dig the book out and check. I think the conclusion of the book was that space is a "something" Not an aether, but something that actually does warp and bend. But if Gravity is just some kind of graviton field you could say that objects are attracted to each other much like magnets attract metal, and space would again just be nothing but space. It is said however that space bends. When Eddington observed the bending of light around the sun during the eclipse it does seem to show that space is bent. Light curved around the sun. What about space tearing operations like flop transitions? Space can be ripped and torn and spliced. How can empty space that has no "actual" existence tear? I would really like to know if indeed space is a something or not.

26. Originally Posted by Liongold
This is really easy to get backwards. If I age 1 year, in an amount of time while you age 10 years.... my eyes will have only seen one year worth of motion.

If we're watching the same tree (from a good distance away), and we both watch it over what you perceive as 10 years.. And the tree were to grow a foot per year (I don' t know what kind of tree does that)... We both see it reach 10 feet.

However: I think it took 1 year to grow 10 feet. You think it took 10 years.

The same analogy would hold for ordinary motion. If you perceive that a car took 20 seconds to cross an area of road, I would perceive that it took 2 seconds to cross the same distance.
Slowing of time means your clock ticks slower. It doesn't mean that distant events appear to happen slower. It's the local events that are happening slower. Distant events appear to happen at the normal speed, but since you yourself are a local event, you think it's the other way around.

So:

1) - The reality:

Everything stayed at its normal speed. You slowed down.

2) - The perception:

You stayed at your normal speed. Everything else sped up.

Relativity does not affect the rate at which information from a distant event arrives, only the rate at which you, yourself, take in information. You're taking in the information slower, which makes it feel like the information is coming at you faster.

What I mean is that, if you finished accelerating by the time you reach Pluto, and you look at Proxima from your space ship, it looks much closer than 4 light years, even though it's still nearly 4 light years away from Earth's perspective.
Correct. But the distance will still seem longer to the people in motion, even though it is shorter than before, as you say.
No. In the 4+ years (because they're moving somewhat slower than C), that they spend heading toward Proxima Centauri, they will age substantially less than 4 years.

You can't age 2 or 3 years, but experience 4+ years. If you experienced 4+ years, then you would have aged 4+ years. It's like taking a movie that's 2 hours long and watching it in 1 hour. You can do this if you watch the whole thing on a fast forward setting. If you watched in on a slow setting it would take longer than 2 hours, not less than 2 hours.

27. Originally Posted by Liongold
You got that completely backwards.

The formula is

where T is the time that passes for our observer "at rest" and t is the time that passes for the "moving" observer. So when v = 0.866c , one second for our "moving" observer equal 2 sec for our observer "at rest".
Janus, I'm usually not one to disagree with you, but are you sure you've got the formula right? As I recall, it should be:

t' = T / sqrt. 1 - v^2/c^2

where t' is the time that passes for the observer in motion and T is the time that passes for an observer at rest, and not the other way around.

From this formula, it is easy to deduce that since the denominator decreases, the result will be a larger value of t for the observer in motion.

Wikipedia, at least, seems to agree that the formula is the way I have just stated it to be:

http://en.wikipedia.org/wiki/Time_dilation
Other than the swicthing of the "prime" symbol, there is nothing in there that disagrees with me.

I think that the issue here is that they say:

T is the time interval between those same events, as measured by another observer, inertially moving with velocity v with respect to the former observer,

What they mean here is that the two observers have a relative velocity with respect to each other and not that one observer is "moving" and the other is not.

They could have equally said:

T is the interval between those same events, as measured by another observer, to which the former observer is interially moving in respect to with a velocity of v.

The second way is just a little more awkward.

The point being is that the clock making the measurement is generally considered the clock at rest, and it is the other clock that is moving, runs slower and registers the least time.

One rule of Relativity to keep in mind is the "Relativistic effects never happen to you, they always happen to the frame which has a mutual relative motion to you."

28. [quote="Liongold"]
Correct. But the distance will still seem longer to the people in motion, even though it is shorter than before, as you say.
No, it will not. You are trying to treat this as if there is such a thing as absolute motion, and there isn't. The "people in motion" consider themselves "at rest" and see the universe move past them. As a result, according to their measurements, the universe contracts, and the distance becomes shorter.

Or to put it another way, the fact that we measure the people and the ship to have length contracted, has no effect on how they measure or perceive things.

Relativity always happens to the "other" guy.

29. Why say that space bends if it doesn't? Isn't there a better way to put that if it's just mathematical. In Brian Greens Book the fabric of the cosmos he brings up the debate of whether or not space is a "something" or not by using the thought experiment of the spinning bucket. If there was a bucket of water alone in space and was spinning would the water take on a concave shape? I think the conclusion was that it would, I'll have to dig the book out and check. I think the conclusion of the book was that space is a "something" Not an aether, but something that actually does warp and bend. But if Gravity is just some kind of graviton field you could say that objects are attracted to each other much like magnets attract metal, and space would again just be nothing but space. It is said however that space bends. When Eddington observed the bending of light around the sun during the eclipse it does seem to show that space is bent. Light curved around the sun. What about space tearing operations like flop transitions? Space can be ripped and torn and spliced. How can empty space that has no "actual" existence tear? I would really like to know if indeed space is a something or not.
No. Space isn't something material at all.

And the bucket thought experiment you refer to comes from Newton's Principia, the result of which Newton concluded was proof that something called absolute space exists. However, if you know your relativity, you should know that absolute space does not exist; relativity was one of the main factors in its removal from the mainstream.

In fact, the conclusion of the bucket thought experiment is that there really is no conclusion; Newton considered it to be proof that an absolute space existed and that the water was rotating relative to it. However, the advent of relativity meant that this was false. All that can be derived from this, in fact, is the notion that rotation is not really a form of relative motion.

The concept of space-time curving is only a useful analogy to explain what happens. True, such curving does happen, but only in a mathematical sense; the tensor equations require us to think of a space-time that curves. Space-time does not physically bend.

Slowing of time means your clock ticks slower. It doesn't mean that distant events appear to happen slower.
And that is where we must disagree. The concept of your clock slowing down is equal to distant events appearing to take a longer time to be fully finished. If you don't believe me, I'd like to point out that when you say:

1) - The reality:

Everything stayed at its normal speed. You slowed down.

2) - The perception:

You stayed at your normal speed. Everything else sped up.
The reality is actually that everything stays at its normal speed while you sped up. If you didn't, why on earth are we talking about acceleration then?

From this, you can easily see that the perception should then translate to you thinking you are at the same speed while everything else has slowed down, in terms of speed.

So, yes, time slowing down does translate to distant events appearing to take longer to complete. You can see it will work out the same way if you were to imagine the following yourself:

Let us define time to be the amount of time taken for a photon to reach us. Not a strict definition, but good enough for our purposes.

Now, obviously, we can say that time passes smoothly at the same rate when a photon hits us at rest. Now, imagine suddenly accelerating to a certain velocity slower than c. Obviously, the light will take longer to reach us, because we are moving away from it, and the light must cover the extra distance we have moved as it was moving to us. And, because of our definition, we have just experienced time dilation.

Now, think of it this way. Light contains information. Consequently, at rest, since you were experiencing time at its fastest, distant events seemed to happen at their usual pace, because light from those events would reach you one after the other. But the situation will be markedly different if you were to accelerate. Now, since light will take a longer time to reach you, the information will take a longer time to reach you, and hence you will see events take a longer time to complete. In a way, those events have slowed down, but only to you.

Relativity does not affect the rate at which information from a distant event arrives, only the rate at which you, yourself, take in information. You're taking in the information slower, which makes it feel like the information is coming at you faster.
Correct. However, your last sentence is wrong. If you're taking in the information slower, this does not mean that you feel it is coming to you faster. The speed of digesting information does not affect the perceived rate at which it is coming. I've already explained why if time slows down, this translates to you thinking that events seem to be taking longer to complete; this I've done through two different ways above. Read them, please.

No. In the 4+ years (because they're moving somewhat slower than C), that they spend heading toward Proxima Centauri, they will age substantially less than 4 years.

You can't age 2 or 3 years, but experience 4+ years. If you experienced 4+ years, then you would have aged 4+ years. It's like taking a movie that's 2 hours long and watching it in 1 hour. You can do this if you watch the whole thing on a fast forward setting. If you watched in on a slow setting it would take longer than 2 hours, not less than 2 hours.
Forgive me, but how does this discussion on age connect with the issue of distance we were discussing?

30. Originally Posted by Liongold

The concept of space-time curving is only a useful analogy to explain what happens. True, such curving does happen, but only in a mathematical sense; the tensor equations require us to think of a space-time that curves. Space-time does not physically bend.
This statement is just ridiculous, and demonstrates nothing except total ignorance of the relevant physics and mathematics.

Of course space does not bend in the manner of a fly rod. Space is not a material object.

But space-time is descrived by a Lorentzian metric and associated connection that most definitely demonstrate curvature. It is that curvature that accounts for what we call gravity.

This is NOT an anaology. It is quite real. It is what keeps your feet attached to the earth (if indeed you have such an anchor point).

Curvature of space-time is just as real as curvature of the surface of the Earth. If you follow a geodesic on the surface of the Earth you don't follow a Euclidean line and if you follow a geodesic in space-time near a massive body you don't follow a Euclidean line either.

Slowing of time means your clock ticks slower. It doesn't mean that distant events appear to happen slower.
And that is where we must disagree. The concept of your clock slowing down is equal to distant events appearing to take a longer time to be fully finished. If you don't believe me, ...
You quite simply do not know what you are talking about. Distance in and of itself does result in any effect on the transformation of time. Time transforms with speed and location, following the Lorentz transformation, between two inertial reference frames in relative motion. Without relative non-zero motion there is no dilation of time nor contraction of length.

You have managed to completely distort the special theory of relativity. Basically you are all wet. Please go learn something about the subject.

Wolfgang Rindler's book Introduction to Special Relativity would be a good place to start. Failing that this Wiki article is pretty good.

http://en.wikipedia.org/wiki/Special_relativity

31. This statement is just ridiculous, and demonstrates nothing except total ignorance of the relevant physics and mathematics.

Of course space does not bend in the manner of a fly rod. Space is not a material object.

But space-time is descrived by a Lorentzian metric and associated connection that most definitely demonstrate curvature. It is that curvature that accounts for what we call gravity.

This is NOT an anaology. It is quite real. It is what keeps your feet attached to the earth (if indeed you have such an anchor point).

Curvature of space-time is just as real as curvature of the surface of the Earth. If you follow a geodesic on the surface of the Earth you don't follow a Euclidean line and if you follow a geodesic in space-time near a massive body you don't follow a Euclidean line either.
DrRocket, if you would care to read my previous explanation of why I'm saying that space-time does not physically curve, I see no reason why we should be arguing. I realise that to you it appears complete gibberish; however, I implore you to try and read what I have written again.

Nevertheless, it is rude to direct you to another post without at least responding humanely to your comments, so I shall do so.

This statement is just ridiculous, and demonstrates nothing except total ignorance of the relevant physics and mathematics.
No offense, DrRocket, but if you could keep the personal allusions to a minimum, it would be conducive to a civilised atmosphere between us.

Of course space does not bend in the manner of a fly rod. Space is not a material object.
Precisely what I have been trying to say: space is not a physical object that can bend physically. It bends in a mathematical sense. Your own statements seem to point to this:

But space-time is described by a Lorentzian metric and associated connection that most definitely demonstrate curvature. It is that curvature that accounts for what we call gravity.
Is not a Lorentzian metric mathematical? Do not the tensor equations that describe the curvature of space belong to mathematics? This is what I mean by a mathematical concept: a rigidly defined and abstract concept. In that sense, the curvature of space-time is a mathematical concept; hence, its associated curvature is also a mathematical concept.

Please, listen to me. I am not saying that such curvature is not real; all I am trying to say is that it is not a physical object.

This is NOT an anaology. It is quite real. It is what keeps your feet attached to the earth (if indeed you have such an anchor point).
All right, DrRocket, I'll concede this one. I meant analogy in the sense that it is a good way to describe the meaning of the mathematics of general relativity; however, that is besides the point now.

Curvature of space-time is just as real as curvature of the surface of the Earth. If you follow a geodesic on the surface of the Earth you don't follow a Euclidean line and if you follow a geodesic in space-time near a massive body you don't follow a Euclidean line either.
Again, DrRocet, I do not mean that the curvature is not real; all I'm trying to say is that the curvature is not physical.

You quite simply do not know what you are talking about. Distance in and of itself does result in any effect on the transformation of time. Time transforms with speed and location, following the Lorentz transformation, between two inertial reference frames in relative motion. Without relative non-zero motion there is no dilation of time nor contraction of length.

You have managed to completely distort the special theory of relativity. Basically you are all wet. Please go learn something about the subject.

Wolfgang Rindler's book Introduction to Special Relativity would be a good place to start. Failing that this Wiki article is pretty good.
You quite simply do not know what you are talking about. Distance in and of itself does result in any effect on the transformation of time. Time transforms with speed and location, following the Lorentz transformation, between two inertial reference frames in relative motion. Without relative non-zero motion there is no dilation of time nor contraction of length.
I think, DrRocket, that if you were to look at the statement of mine you have quoted here, you would see it has nothing to do with distance. Kojax and I were merely discussing time dilation, in that I was attempting to say that the notion of time dilation, or, in easier language, the slowing down of time for an observer in motion, meant that the observer would think that events were taking a longer time to complete or, indeed, merely occur; he, on the other hand, thought that to the observer, it would appear that events were taking a smaller amount of time to occur, meaning that events would appear to be happening faster for the observer. In no way does distance come into our discussion.

That said, DrRocket, I cannot deny your statements; they are, as they almost always are, correct. I'm only confused as to how it applies to my statements. I would be most grateful if you could clarify.

You have managed to completely distort the special theory of relativity. Basically you are all wet. Please go learn something about the subject.
DrRocket, I doubt anyone appreciates personal allusions. I realise your opinion of my understanding of relativity is low, but surely there is no call to be rude. If you truly think I do not understand, or in your words, have distorted, any subject, I would appreciate it if you could correct me where I am wrong. You have done so on previous occasions, and for that, I am grateful, and even more so for the numerous references you have provided for further information. All I am asking, DrRocket, is civility between us; nothing more, nothing less.

Nonethless, DrRocket, there may be some truth to your words. After all, my understanding of relativity is based purely on concepts, the quality of which is for others to decide; the mathematics of relativity, however, would require me to first graduate and then go off to university. Given that I am only 15, that may be a little hard, especially in my current position.

Nonetheless, I have taken your advice into account, and I assure you, DrRocket, that I will do just as much as possible to really understand relativity, at the very least up to your standards.

Wolfgang Rindler's book Introduction to Special Relativity would be a good place to start. Failing that this Wiki article is pretty good.

http://en.wikipedia.org/wiki/Special_relativity
Thank you for the references.

32. Originally Posted by Janus
Originally Posted by Liongold
You got that completely backwards.

The formula is

where T is the time that passes for our observer "at rest" and t is the time that passes for the "moving" observer. So when v = 0.866c , one second for our "moving" observer equal 2 sec for our observer "at rest".
Janus, I'm usually not one to disagree with you, but are you sure you've got the formula right? As I recall, it should be:

t' = T / sqrt. 1 - v^2/c^2

where t' is the time that passes for the observer in motion and T is the time that passes for an observer at rest, and not the other way around.

From this formula, it is easy to deduce that since the denominator decreases, the result will be a larger value of t for the observer in motion.

Wikipedia, at least, seems to agree that the formula is the way I have just stated it to be:

http://en.wikipedia.org/wiki/Time_dilation
Other than the swicthing of the "prime" symbol, there is nothing in there that disagrees with me.

I think that the issue here is that they say:

T is the time interval between those same events, as measured by another observer, inertially moving with velocity v with respect to the former observer,

What they mean here is that the two observers have a relative velocity with respect to each other and not that one observer is "moving" and the other is not.

They could have equally said:

T is the interval between those same events, as measured by another observer, to which the former observer is interially moving in respect to with a velocity of v.

The second way is just a little more awkward.

The point being is that the clock making the measurement is generally considered the clock at rest, and it is the other clock that is moving, runs slower and registers the least time.

One rule of Relativity to keep in mind is the "Relativistic effects never happen to you, they always happen to the frame which has a mutual relative motion to you."
I apologise, Janus. I did not happen to see your post previously, hence my rather late reply to it.

I think that the issue here is that they say:

T is the time interval between those same events, as measured by another observer, inertially moving with velocity v with respect to the former observer,

What they mean here is that the two observers have a relative velocity with respect to each other and not that one observer is "moving" and the other is not.
Not something I can argue with. That is certainly correct.

They could have equally said:

T is the interval between those same events, as measured by another observer, to which the former observer is interially moving in respect to with a velocity of v.

The second way is just a little more awkward.

The point being is that the clock making the measurement is generally considered the clock at rest, and it is the other clock that is moving, runs slower and registers the least time.

One rule of Relativity to keep in mind is the "Relativistic effects never happen to you, they always happen to the frame which has a mutual relative motion to you."
That I understand, and know; I usually rephrase that as being equivalent to Galileo's principle of relativity. I find it an easier statement to work with.

No offense, but while what you say is true, how exactly does it tie in with my original statements? If you recall, I was attempting to point out that the value of t' grows as velocity increases.

33. Originally Posted by Liongold

Nonethless, DrRocket, there may be some truth to your words. After all, my understanding of relativity is based purely on concepts, the quality of which is for others to decide; the mathematics of relativity, however, would require me to first graduate and then go off to university. Given that I am only 15, that may be a little hard, especially in my current position.
If you are only 15 then you are at least showing and admirable tendency toward thinking for yourself.

However, you still have the theory scrambled. You would do much better to talk and type less and read and listen more. When you do type, it would be better to ask questions than to state incorrect facts and misleding ideas and argue for their validity.

There is an unfortunate fact, that many of the wackos who advocate "non mainstream" physics on the internet also think independently, but they don't think logically and they don't understand the theories that they criticize. It is important that in your formative years you learn what is actually known and how the theories actually work. Some of those theories are a bit counter-intuitive, especially relativity. If ingrain yourself with misconceptions regarding the basic theories of physics, then you will have great difficulty correcting those notions later on when you are better prepared to learn the material in detail. Be careful, you are on a slippery slope. It is not too late to get back on track, but the momentum is in the wrong direction at this point in time.

The mathematics of special relativity is not difficult. It requires only a little algebra. You ought to be able to read the book that I mentioned and the Wiki article with just some hard work.

General relativy is an entirely different story. That requires quite a bit of deep mathematics. Einstein needed a lot of help with it himself.

34. [quote="Janus"]
Originally Posted by Liongold
Correct. But the distance will still seem longer to the people in motion, even though it is shorter than before, as you say.
No, it will not. You are trying to treat this as if there is such a thing as absolute motion, and there isn't. The "people in motion" consider themselves "at rest" and see the universe move past them. As a result, according to their measurements, the universe contracts, and the distance becomes shorter.

Or to put it another way, the fact that we measure the people and the ship to have length contracted, has no effect on how they measure or perceive things.

Relativity always happens to the "other" guy.
So basically you mean to say that to the people in motion, the distance has actually grown shorter, rather than longer?

But how is that so? More precisely, in the following thought experiment:

If a rocket moving at a speed close to c, which we denote as v, time dilation occurs; we denote the time measured by an observer at rest relative to the rocket as t, and the time measured by the crew of the rocket will be t'. The distance to Proxima Centauri we write as equal to D.

Obviously, the speed is measured by

v = D/t

from the point of somone at rest.

It follows that the observers must measure the same speed, because if it wasn't, they would feel accelerational effects; however, the time dilation issue poses a problem. The only way to solve this will be to observe another distance, which we call D', [which must be longer so as to counter the growth in the value of t'].

Therefore,

v = D'/t'

Which is why the observers are not permitted to measure the same distance [or even a shorter distance, as this would imply a change in the speed. Consequently, the only distance they can measure is a longer one] . If they did, they would have to feel acceleration, which is impossible.
Note: All statements in [] are statements I added to the quoted piece to make it more relevant to this discussion.

So, are you saying there is a flaw in my reasoning here in this thought experiment? If so, could you please tell me what it is?

Also, I am a bit surprised at this. Relatively speaking, if we look at this as a situation involving someone at rest (hereafter called A) and someone in motion (hereafter called B), then A can say that B has contracted in length. In order for the principle of relativity to hold intact, this should mean that B can also say that he is still the same length but that everything is now longer than before; more specifically, the distance he is travelling has just gotten longer.

If you could please tell me where I went wrong in the above scenarios, I would be most grateful.

35. Originally Posted by DrRocket
Originally Posted by Liongold

Nonethless, DrRocket, there may be some truth to your words. After all, my understanding of relativity is based purely on concepts, the quality of which is for others to decide; the mathematics of relativity, however, would require me to first graduate and then go off to university. Given that I am only 15, that may be a little hard, especially in my current position.
If you are only 15 then you are at least showing an admirable tendency toward thinking for yourself.

However, you still have the theory scrambled. You would do much better to talk and type less and read and listen more. When you do type, it would be better to ask questions than to state incorrect facts and misleding ideas and argue for their validity.

There is an unfortunate fact, that many of the wackos who advocate "non mainstream" physics on the internet also think independently, but they don't think logically and they don't understand the theories that they criticize. It is important that in your formative years you learn what is actually known and how the theories actually work. Some of those theories are a bit counter-intuitive, especially relativity. If ingrain yourself with misconceptions regarding the basic theories of physics, then you will have great difficulty correcting those notions later on when you are better prepared to learn the material in detail. Be careful, you are on a slippery slope. It is not too late to get back on track, but the momentum is in the wrong direction at this point in time.

The mathematics of special relativity is not difficult. It requires only a little algebra. You ought to be able to read the book that I mentioned and the Wiki article with just some hard work.

General relativy is an entirely different story. That requires quite a bit of deep mathematics. Einstein needed a lot of help with it himself.
If you are only 15 then you are at least showing an admirable tendency toward thinking for yourself.
Thank you, DrRocket.

Also, I have a collection of Einstein's original papers here at home. Do you suppose that I should attempt to read them as well, or that I should preferably leave them until after reading the two you have suggested?

36. Originally Posted by Liongold

Also, I have a collection of Einstein's original papers here at home. Do you suppose that I should attempt to read them as well, or that I should preferably leave them until after reading the two you have suggested?
It never hurts to read the papers from the original "giants". But how much good it will do initially I don't know, as Einstein is not always the most clear expositor, at least to me, due to the perspective and presentation that was typical during the time that he was active.

If it were me I would first read Rindler's book and then read the original Einstein. But it is a matter of personal perspective and choice. I just find the more modern presentation cleaner and easier to follow, but that is probably due to my own personal background -- I look at the issues from the perspective of a mathematician, and like a more or less axiomatic treatment because of the clarity that it brings to the fundamental assumptions and the logic that is applied to reach the deeper conclusions from them.

You can't go too far wrong by readijng Einstein himself.

Another treatment that you might like is in The Feynman Lectures on Physics by Feynman, Leighton and Sands. This is an edited compilation of a set of lectures given by Feynman over a couple of years to a freshman/sophomore physics at Cal Tech in the early 1960's. It is a stupendous book, one of the best physics books ever written. The treatment of special relativity is just as good as the rest of the book (3 volumes). It is not cheap, but it covers virtually all of physics from a simple perspective, and is an excellent reference for future studies beyond just relativity.

37. Originally Posted by Liongold
Slowing of time means your clock ticks slower. It doesn't mean that distant events appear to happen slower.
And that is where we must disagree. The concept of your clock slowing down is equal to distant events appearing to take a longer time to be fully finished. If you don't believe me, I'd like to point out that when you say:
No. This is exactly the mistake. Your clock slowing is not equal to distant events appearing to take longer. Not at all. There is no perspective from which that can be true.

How long you think something took == how far the hands on your clock moved.

How far are they moving when they go slow? How far are they moving when they go fast?

1) - The reality:

Everything stayed at its normal speed. You slowed down.

2) - The perception:

You stayed at your normal speed. Everything else sped up.
The reality is actually that everything stays at its normal speed while you sped up. If you didn't, why on earth are we talking about acceleration then?

In relativity, "you" didn't speed up. Your rate of travel increase, but that didn't cause your body to uniformly start doing everything faster. Your perception of time doesn't change when you're in a sports car going 100 mph.

In relativity, "you" slow down, and this is a separate thing from your overall rate of travel. Imagine how fast a turtle thinks events are happening around him. To him, 10 mph is probably super fast.

Let us define time to be the amount of time taken for a photon to reach us. Not a strict definition, but good enough for our purposes.

Now, obviously, we can say that time passes smoothly at the same rate when a photon hits us at rest. Now, imagine suddenly accelerating to a certain velocity slower than c. Obviously, the light will take longer to reach us, because we are moving away from it, and the light must cover the extra distance we have moved as it was moving to us. And, because of our definition, we have just experienced time dilation.
You're going to want to really examine carefully your understanding of this particular point, because this is where time dilation comes out of, for the most part.

You know of the Michealson-Morley experiment?

Think about the basis for that experiment, and you'll see how time dilation works. It's about light taking longer to complete round trips.

If the path is up-down, down-up, then it has to take a diagonal path to reach the detector (or the detector would move out of the way during the trip, and it would miss).

If the path is forward-backward, backward-forward, then it spends less total time going backward than it does going forward.

Basically information about changes in motion are carried by photons, or things like photons (gravitons, etc) in some sense or another, and so all events occurring in a fast moving frame of reference have to actually happen slower (because the photons have to take longer to arrive) Events outside that frame of reference, on the other hand, are free to actually happen at a faster rate.

Now, think of it this way. Light contains information. Consequently, at rest, since you were experiencing time at its fastest, distant events seemed to happen at their usual pace, because light from those events would reach you one after the other. But the situation will be markedly different if you were to accelerate. Now, since light will take a longer time to reach you, the information will take a longer time to reach you, and hence you will see events take a longer time to complete. In a way, those events have slowed down, but only to you.
This is where the part about "round trips" becomes important. There are no round trips between you and a star 100 light years away, so relativity doesn't cause those events to slow. (I mean, if the star is moving near C as well, it will be slower, but that would be true even if you weren't moving near C)

Only events near enough that light has to make a round trip, in order for you to perceive them will become uniformly slower. In particular, events you could interact with other than just by observation, are affected. IE. events considered to be part of your "inertial frame" are the only ones considered to slow.

38. Originally Posted by kojax

In relativity, "you" didn't speed up. Your rate of travel increase, but that didn't cause your body to uniformly start doing everything faster. Your perception of time doesn't change when you're in a sports car going 100 mph.
This simple statement demonstrates the crux of the difficulty that is being discussed.

The reason that it is correct is that it relates to one single observer in one particular inertial reference frame -- a car traveling at a fixed speed.

That sports car is NOT going 100 mph, it is perhaps traveling at 100 mph with respect to an observer who is at rest relative to the road. It is going several thousand mph with respect to an observer who is at rest relative to the sun. Relative to an observer sitting the passenger seat, the driver is not moving at all. And relative to that observer in the car, time and distance are quite normal, even if the car is approaching the speed of light relative to some other reference frame.

The point is that you cannot talk about time or length without first specifying the reference frame in which they are to be measured. And to use special relativity you need to be certain that the reference frame is inertial. Not all reference frames are inertial (in fact it is probably impossible to find one that is truly inertial but there are lots of good approximations).

Relativity speaks to the differences in time and spatial measurements made by two observers in inertial reference frames that are in uniform motion with respect to one another. Nothing more and nothing less.

A key difference between special relativity and general relativity is that in special relativity the background includes a universal reference frame so that time and space are clearly defined concepts, and so that there is a notion of universal time in any single inertial reference frame that you choose. In general relativity space-time is a curved manifold and there are no universal coordinates, and hence no clear definition of either time or space that applies to points that are distant from one another. It would be advisable to limit the discussion here to the implications of special relativity.

39. Originally Posted by Liongold

So, are you saying there is a flaw in my reasoning here in this thought experiment? If so, could you please tell me what it is?

Also, I am a bit surprised at this. Relatively speaking, if we look at this as a situation involving someone at rest (hereafter called A) and someone in motion (hereafter called B), then A can say that B has contracted in length. In order for the principle of relativity to hold intact, this should mean that B can also say that he is still the same length but that everything is now longer than before; more specifically, the distance he is travelling has just gotten longer.

If you could please tell me where I went wrong in the above scenarios, I would be most grateful.

Let's do an example:

B travels from A to C, a distance of 7 light hours as measured by A, at a velocity with respect to A (and C) of v equal to 0.99c

This takes a time of just over 7 hours as measured by A: We will call this time tA.

Now we use the time dilation formula to determine how long this will be for B:

The thing to note here is that the formula gives how much time "your" clock ticks compared to the other clock. Since we already know that, we re-arrange to solve for the other clock (in this case B):

Plugging in our known values, we get a little over 1 hr of time that ticks off for clock B according to A.

Now A and B have to agree as to how much time passes on clock B during the trip. Assume that A & B both take photos when B is at A and at C. When B is at A both photos show that Clock B reads 0. And when B is at C they both show that B reads 1 hr (Otherwise you would have two photos of the same event that showed two different things.)

Now it is obvious that B cannot cross a seven light hour distance in 1 hr and still only have a relative velocity of 0.99c, So in order for B to measure the relative velocity between it and A as being 0.99c, the distance between A and C must shrink to 1 light hour as measured by B.

You mentioned the Principle of Relativity. The thing is, according to it, you can not tell which, between two inertial frames is really "moving". In fact, the question becomes meaningless.

But if your interpretation of events where correct, you could easily tell who is really moving, as that would be the frame which measures distances in the stationary frame as being longer, and the stationary frame would be the one which saw the moving frame as contracted.

As it is, both frames measure the other as contracted, and there is no way to tell which is "moving".

40. This may be a stupid question, but is gravity the only force that can
bend space time?

41. Originally Posted by kojax
I'm not sure that's how Lorentz contraction works.
http://en.wikipedia.org/wiki/Special_relativity

42. Originally Posted by dedo
This may be a stupid question, but is gravity the only force that can
bend space time?
Gravity IS the curvature of space-time.

43. One thing I can't quite get my head around is how exactly curvature causes gravity. I mean, I can easily imagine it to be like a bobsled following a path, but how is it that how massive the body is travelling through the gravity well can affect how much it is deviated by it? If Einstein had said that gravity equates to density, it would have been easier to imagine, i.e. that mass causes a higher or lower "density" of "space-time" in its proximity or something.

The stretched cloth with a marble in the middle does not do the job, since the curvature is illustrated by the indentation, but to illustrate how gravity affects a mass that travels through the well (by rolling another marble across it), you still need gravity as a force to account for it.

Know what I mean? The inertia associated with mass would be an answer, but is that enough of an answer?

44. If gravity is curvature of space time, then in the papers on advanced propulsion theory (warp bubbles etc.), the authors try to drive a ship with a contracted/expanding "wave" of space time.

This is supposed to require enormous energy. Thus, the authors seem to believe that they can "warp" space time with energy, not mass.

What does this have to do with gravity? Are there any examples in nature where space time is warped/curved with energy, not mass (other than the big bang)?

45. Originally Posted by dedo
If gravity is curvature of space time, then in the papers on advanced propulsion theory (warp bubbles etc.), the authors try to drive a ship with a contracted/expanding "wave" of space time.

This is supposed to require enormous energy. Thus, the authors seem to believe that they can "warp" space time with energy, not mass.

What does this have to do with gravity? Are there any examples in nature where space time is warped/curved with energy, not mass (other than the big bang)?
Don't confuse "papers on advanced propulsion theory" with science fiction, which I suspect is what you are talking about. There has even been some stuff like this that has appeared in JANAF and AIAA conference papers -- and it is still not real propulsion but more in the nature of science fiction.

The only (partial) exception of which I am aware is Alcubierre drive which is extremely speculative and not a serioius propulsion system but rather a study of a rather unusual aspect of general relativity.

http://en.wikipedia.org/wiki/Alcubierre_drive

Mass and energy are the same thing, () so it is possible to relative curvature to energy as well as mass, but it takes a LOT of energy. You can even theoretically have a stable gravitational structure created by energy. Such structures were studied by John Archibald Wheeler, who called them geons.
http://en.wikipedia.org/wiki/Geon_(physics)

But none of this is the stuff of real propulsion systems, advanced or otherwise. Authors of science fiction take a great deal of license with science itself in order to make a good story. There is nothing wrong with that, so long as you don't confuse the story with real science.

46. Originally Posted by DrRocket
Originally Posted by dedo
If gravity is curvature of space time, then in the papers on advanced propulsion theory (warp bubbles etc.), the authors try to drive a ship with a contracted/expanding "wave" of space time.

This is supposed to require enormous energy. Thus, the authors seem to believe that they can "warp" space time with energy, not mass.

What does this have to do with gravity? Are there any examples in nature where space time is warped/curved with energy, not mass (other than the big bang)?
Don't confuse "papers on advanced propulsion theory" with science fiction, which I suspect is what you are talking about. There has even been some stuff like this that has appeared in JANAF and AIAA conference papers -- and it is still not real propulsion but more in the nature of science fiction.

The only (partial) exception of which I am aware is Alcubierre drive which is extremely speculative and not a serioius propulsion system but rather a study of a rather unusual aspect of general relativity.

http://en.wikipedia.org/wiki/Alcubierre_drive

Mass and energy are the same thing, () so it is possible to relative curvature to energy as well as mass, but it takes a LOT of energy. You can even theoretically have a stable gravitational structure created by energy. Such structures were studied by John Archibald Wheeler, who called them geons.
http://en.wikipedia.org/wiki/Geon_(physics)

But none of this is the stuff of real propulsion systems, advanced or otherwise. Authors of science fiction take a great deal of license with science itself in order to make a good story. There is nothing wrong with that, so long as you don't confuse the story with real science.
Thanks DrRocket!

I was referring to the Alcubierre drive. However, this drive, and modifications of this drive, all seem to require massive energy.

I don't have the reference handy but, I think some people have speculated that there may be other drives that emerge other than the Alcubierre drive and the worm hole idea.

I was wondering if:

1. Gravity can curve space time.
2. Gravity depends on mass and spin (frame dragging)

Is is possible to build an engine based on spin?

The question then becomes: what do you spin?

Here is a link to an article about gravitational fields in rotating superconductors.

arxiv.org/pdf/gr-qc/0607086

I wonder if this is what they are getting at eg. warping space time w/ spin???

If spin works, at least it is something you might be able to design experiments around. Just start spinning things and see which one "warps out of sight".

47. Originally Posted by dedo

I was wondering if:

1. Gravity can curve space time.
2. Gravity depends on mass and spin (frame dragging)
Gravity IS the effect of curved space time. But associated with gravity is energy, potential energy, and energy and mass are equivalent and can influence the curvature of space-time. So, yes, there can be a "feedback loop". This is recognized in vacuum solutions to the Einstein field equations.

http://en.wikipedia.org/wiki/Vacuum_solution_(general_relativity)

Is is possible to build an engine based on spin?

The question then becomes: what do you spin?
A Wankel engine ? 8) Other than that I don't know what you mean by "an engine" in this context.

Here is a link to an article about gravitational fields in rotating superconductors.

arxiv.org/pdf/gr-qc/0607086

I wonder if this is what they are getting at eg. warping space time w/ spin???

If spin works, at least it is something you might be able to design experiments around. Just start spinning things and see which one "warps out of sight".
I don't know what they are driving at in that paper and don't have the time or ready expertise to evaluate it. I do note that it does carry any reference to any submittal to a peer refereed journal. That makes me slightly suspicious.

I would be pretty willing to be that no propulsion system will come of this in our lifetime.

There are a lot of things that are spinning, some, like some neutron stars, are pretty massive and spinning pretty fast. Nothing has "warped out of sight yet".

48. Thanks Dr. Rocket,

I think I should study Dr. Wheeler's arguments and people who have cited his paper.

Much of this is over my head; however, the best papers have discussions that really explain the concepts well.

I also am not aware of any observation in nature or experiments where FTL has been observed. However, if something moved faster than light such as a "wave" of space time after an explosion, or from a spinning star, it might be hard to "see".

I just fundamentally think that a riding some kind of "wave of contracted/warped space" is not the way. The energy requirements are too high. Also, I have not seen anyone propose an argument of how to use the massive energy to create a warp, even if you could generate the energy.

49. So who thinks space actually bends and who says its just a abstract? Also what is happening with potential energy. If you are at the top of a roller coaster you have more energy/mass than you do at the bottom right. so the higher you go up the more potential energy you have. but at some point the potential energy must stop increasing and start to decrease as the force of gravity becomes weaker. What governs this potential energy?

50. Originally Posted by Wildstar
So who thinks space actually bends and who says its just a abstract? Also what is happening with potential energy. If you are at the top of a roller coaster you have more energy/mass than you do at the bottom right. so the higher you go up the more potential energy you have. but at some point the potential energy must stop increasing and start to decrease as the force of gravity becomes weaker. What governs this potential energy?
"Bend" and "stretch" are words from our everyday experiences that physicists sometimes use to convey the very technical concept of "Riemannian curvature" which unfortunately has no precise everyday analogy.

51. Space-time is actually stretching according to Cosmological inflation models. Of course no one quite knows the reason why.

All we have at this point are hypothesis.

52. Originally Posted by Latin_of_delight
Space-time is actually stretching according to Cosmological inflation models. Of course no one quite knows the reason why.

All we have at this point are hypothesis.
What is "stretching" are space-like slices of space-time, if such even exist.

Space-time itself, according to general relativity, is the whole enchilada. All of space, all of time, all mixed together and inseparable. It contains the past, present, and future all at once, and somewhat scrambled.

Expansion itself is relatively explained as a carry-over from the initial expansion of the big bang. It in fact is predicted by general relativity with a cosmological constant of 0. One would expect that expansion to be slowing due to the gravitationla effect of the mass throughout the universe. Up until about 1998, the big open question in cosmology was whether the mass in the universe would 1) cause the expansion to stop and a re-contraction to start 2) expand at a rate that would lead to cessation of expansion only asymptotically at infinity or 3) simply expand forever with no limiting behavior.

More recent observations of supernova phenomena and subsequently other data, have lead to the conclusion that the rate of expansion of the universe is actually increasing. THAT is what presents the puzzle.

There are some ideas as to what might cause the expansion. It is a bit different from inflation, which is not terrifically well understood beyond depending on some mysterious scalar field. Most of the work of inflation was apparently over well within the first second following the big bang. Of course, now there are new proposals for "eternal inflation".

It turns out that the energy of the vacuum state as predicted by quantum field theories, particularly quantum electrodynamics, results in a negative pressure term that when put into general relativity results in a positive cosmological constant. That is precisely how dark energy is modeled, to explain the accelerating expansion. Unfortunately the calculated vacuum energy exceeds the amount needed to explain the observed expansion by the factor of That is 10000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 000000000000000000000. In some circles that is considered a large error.

What this illustrates is that physics is a vibrant area for research. It also illustrates that "explanations" for questions on the cutting edge ought to be viewed with more that one grain of salt.

53. what do you think about this. The inflaton field that caused the initial expansion is now the cause of the accelerating universe. It started out powerfully and inflated the universe by a massive amount and then the field went down to non zero state and stopped expansion. If the gravitation force somehow suppressed the inflaton field, and as space expanded to near our current size, the inflaton field was able to overpower the effect of gravity and began the inflation anew. So our current accelerated expansion is not due to the quantum fluctuation of space, but is in fact a return of the iinflaton field strength?

54. Originally Posted by Wildstar
what do you think about this. The inflaton field that caused the initial expansion is now the cause of the accelerating universe. It started out powerfully and inflated the universe by a massive amount and then the field went down to non zero state and stopped expansion. If the gravitation force somehow suppressed the inflaton field, and as space expanded to near our current size, the inflaton field was able to overpower the effect of gravity and began the inflation anew. So our current accelerated expansion is not due to the quantum fluctuation of space, but is in fact a return of the iinflaton field strength?
It sounds as though you are animating the inflation field.

What is needed is something to tie the expansion in with the rest of physics.

55. Yeah I was. It's just something I thought about. But isn't that already in inflationary cosmology?

56. Originally Posted by Wildstar
Yeah I was. It's just something I thought about. But isn't that already in inflationary cosmology?
The problem with inflation is that it seems to do a good job of predicting the cosmic background radiation, both the near isotropy and the slight anisotropy, but there is no hint as to what is really going on. It requires a scalar field, the inflation field. But nobody has an inkling what it is. There is only one scalar field that is part of the Standard Model, the Higgs field, and the Higgs field is not the inflation field.

There are also several versions of inflation. The original version had inflation doing its work and being a non-issue within a small fraction of a second. Now there is also something called "eternal inflation".

Now, inflation does seem to be a very promising explanation for a number of thorny issues, among them the horizon problem and the apparent absence of magnetic monopoles. So, it is something worthy of attention. But it is really the start of a good explanation and a good theory and not the culmination. But "I don't know" doesn't sell books and it doesn't give our rather ignorant Congress reason to throw money at physics. Just like politicians, some scientists "spin" the news to keep interest high and money coming in.

One problem is that at the moment that is a lot of speculation and hype regarding advanced, conjectural cutting-edge research physics. That includes strings, M-theory, inflation, eternal inflation, the "multiverse", ad nauseum. There seems to be WAY too much emphasis on people selling books to the general public, and stating conjectures as though they were truths chiseled in stone and handed down from on high. In my opinion it would be a great improvement if there were a lot more emphasis on doing solid research, doing good peer-reviews and making sure that what is published is valid and significant, and a lot less emphasis on speculation without basis and investigating third-tier implications of unproven conjectures. Just for example, I think it would be appropriate that the implications of M-theory not be put out as the next great thing until at least one person on the planet can actually define what M-theory is. Witten laid it out as a plausible conjectural notion in 1995 and it remains a conjecture to this day.

All of this makes for good press, but it is not good science. Feynman would be appalled. He was a strong advocate for scientists being brutally honest with themselves and with the public.

57. I think some of this has to do with getting people excited about physics. People are excited by outrageous things. but I like the speculation from the layman perspective in that I have thought about parallel universes and such for most of my life, and having someone bring the idea from a scientific standpoint kind of validates in a way my thoughts on the subject for so long. but if these ideas do not pan or if I learn of things that supersede what I understand I'm willing to change my philosophy to be more in line with the truth.

58. Originally Posted by Wildstar
I think some of this has to do with getting people excited about physics. People are excited by outrageous things. but I like the speculation from the layman perspective in that I have thought about parallel universes and such for most of my life, and having someone bring the idea from a scientific standpoint kind of validates in a way my thoughts on the subject for so long. but if these ideas do not pan or if I learn of things that supersede what I understand I'm willing to change my philosophy to be more in line with the truth.
There is certainly good in having people interested in and excited by physics.

But it would be more honest if they were excited by the real thing rather than some version cooked up for monetary purposes, whether they be grant monies or book royalties. There is plently of good physics, and hype eventually paints the good and the bad together.

As for parallel universes, that one really bothers me. It appears to be a hypothesis being put forth by a group of people who have utterly failed to produce any physical predictions as a parochial position to justify their own work. The multiverse, whether correct or not, is even in principle, untestable. These "pocket universes" even if they exist, are causally disconnected from our own universe. As such they are perhaps fit topics for philosophy, but not for science.

Your thought process, as you describe it, is exactly the opposite of what is required in science. An theory is accepted if and only if it produces testable predictions that are supported by experimental or observational evidence. An idea the produces no testable predictions or produces predictions that are not supported by experiment is not accepted. So, multiverses are to be at best held as a currently unsupported hypothesis and not as a part of accepted science. Unitil they pan out they are only guesses. It it not what you "believe" that counts, but rather what you can show to be true with hard evidence. Beliefs are what make religion. Data is what makes science.

59. Yeah, I do tend to hold favor with prediction a lot. I don't really know what the hard science says because I've only read books of the popular variety. But I'm gonna check out those books you suggested.

60. space-time is not being curved. as i stated in my gravity theory space isnt empty. if the light has to travel through thicker dark matter towards the curve than it will have to travel through more dark matter. it will appear to take longer. or should i say it will take longer. time does not increase or decrease. we only think it does because if the time things take to happen. space/time isnt curving around everything. dark matter is curving around everything. the expansion of dark matter causes gravity.

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