Gravity and its effect on time

[TheIsland24]

I have tried to understand this concept many times. I have stumbled upon an explanation that I think fits nicely, on a general level. I will use the rocket ship situation to explain. The mass of Earth and the things on it creates a strong gravitational force where space-time is warped considerably. Because time is warped with space, it takes longer to get through time relative to a place with less gravitational pull and "straighter" time. A man on a rocket-ship moving extremely close to the speed of light would be moving farther and farther away from Earth and feel its gravity less and less. The fast speed would limit the effect of gravity. Therefore, space-time, specifically time, would be less warped and straighter. So as this man on the rocket-ship moved through it, he would get through the time quicker than the man on Earth gets through it. To move from one point in time to another in the straight line of space-time on the rocket-ship moving so incredibly fast is quicker than moving through a line of time that is crunched up and curved on earth. Therefore, the man in the rocket-ship gets to the "200 year later mark on earth" in say, only 2 and a half years. If he returns to earth, 200 years may have passed but for him it has only been 2 years. Summed up, the man on the rocket-ship is able to get to 200 years into the future on Earth in only 2.5 years because time for him is straighter and takes less time to move through compared to earth. Can anybody with knowledge of this explain to me if I am on the right track?

 

[nismaratwork]

You're not on the right track.

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

 

[TheIsland24]

I don't trust people who say that I am not on the right track and then give me links to wikipedia.

 

[Dale]

Summed up, the man on the rocket-ship is able to get to 200 years into the future on Earth in only 2.5 years because time for him is straighter and takes less time to move through compared to earth. Can anybody with knowledge of this explain to me if I am on the right track?

You are not too far off, but there are a couple of subtle mistakes. In Minkowski geometry the correct measure of "distance" is the spacetime interval
$$d\tau^2=dt^2-dx^2-dy^2-dz^2$$

From this metric it can be seen that straight lines have the longest interval, not the shortest. So say you have 3 twins that start off in a space station far from any gravitating object. One twin stays, one twin goes and visits the nearest big planet, and one twin goes far away turns around and comes back. The twin that stayed has a straight worldine, the planet twin's worldline curves due to the curvature of gravity, and the far away twin's worldline is not straight because of the sharp turn. Therefore, the staying twin, having traveled straight in spacetime, will have the longest time according to the metric.

 

[nismaratwork]

Oh look, the twin paradox... just as I linked to wikipedia THEISLAND24.

 

[TCS]

I have tried to understand this concept many times. I have stumbled upon an explanation that I think fits nicely, on a general level. I will use the rocket ship situation to explain. The mass of Earth and the things on it creates a strong gravitational force where space-time is warped considerably. Because time is warped with space, it takes longer to get through time relative to a place with less gravitational pull and "straighter" time. A man on a rocket-ship moving extremely close to the speed of light would be moving farther and farther away from Earth and feel its gravity less and less. The fast speed would limit the effect of gravity. Therefore, space-time, specifically time, would be less warped and straighter. So as this man on the rocket-ship moved through it, he would get through the time quicker than the man on Earth gets through it. To move from one point in time to another in the straight line of space-time on the rocket-ship moving so incredibly fast is quicker than moving through a line of time that is crunched up and curved on earth. Therefore, the man in the rocket-ship gets to the "200 year later mark on earth" in say, only 2 and a half years. If he returns to earth, 200 years may have passed but for him it has only been 2 years. Summed up, the man on the rocket-ship is able to get to 200 years into the future on Earth in only 2.5 years because time for him is straighter and takes less time to move through compared to earth. Can anybody with knowledge of this explain to me if I am on the right track?

When you accelerate, you are warping space time. When you are at a constant velocity, other people see you as being smaller and your time as moving slower because you are very heavy. For you, everything around you will be a lot closer and heavier with slower time even though it is all moving very fast. However, there is a far far away region of the universe that has gotten bigger and farther away. To determine exactly what you or any other observer will see, you will also need to account for velocity red shift as well.

 

[Ich]

I think I disagree with everything except the last sentence.

When you accelerate, you are warping space time.

No, you leave spacetime intact and flat.

When you are at a constant velocity, other people see you as being smaller and your time as moving slower because you are very heavy.

No. They see you as increasingly contracted and slower because they use a different coordinate system.

For you, everything around you will be a lot closer and heavier with slower time even though it is all moving very fast.

Lorentz contraction applies only in the direction of motion, not perpendicular to it.

However, there is a far far away region of the universe that has gotten bigger and farther away.

No. Lorentz contraction is not dependent on distance, it's the same everywhere.

 

[TCS]

I think I disagree with everything except the last sentence.

No, you leave spacetime intact and flat.

No. They see you as increasingly contracted and slower because they use a different coordinate system.

Lorentz contraction applies only in the direction of motion, not perpendicular to it.

No. Lorentz contraction is not dependent on distance, it's the same everywhere.

The curvature of space depends upon the stress energy tensor which depends upon the energy contained within a volume. Except for objects perpendicular to you, all objects will shrink. It's not any different than looking at the universe through a magnifying glass that is warped in accordance with energy density and energy flow.

Edit: Although, you are right that it should shrink more in the direction of travel because of the energy flow terms.

Also, the universe is expanding so there are some objects in the universe whose kinetic energy will reduce when you accelerate.

 

[Ich]

The curvature of space depends upon the stress energy tensor which depends upon the energy contained within a volume.

This has (almost) exactly nothing to do with acceleration, and it's not the source of the effects you described.

Except for objects perpendicular to you, all objects will shrink.

No.

Where did you get these ideas from? Can you point to some sources?

 

[TCS]

If you've accelerated from velocity 1 to velocity 2 from the perspective of a non-accelerating observer, you will have felt the acceleration. However, you will still be at velocity zero. This means everything in your neighborhood that didn't acceleratd with you is now moving at a different velocity and if you have increased to 99% the speed of light form your inital frame, than everything around you has a lot of energy. Since energy warps space time, the warping will have occurred when you accelrated. However, for observers you will be warping space time as you move through it.

 

[Ich]

[...]if you have increased to 99% the speed of light form your inital frame, than everything around you has a lot of energy. Since energy warps space time, the warping will have occurred when you accelrated.

It's the same curvature but viewed in a different frame. The curvature is not responsible for Lorentz contraction or time dilation. The coordinate change is.

Again, where did you get these ideas from? I'm genuinely interested.

 

[nismaratwork]

It's the same curvature but viewed in a different frame. The curvature is not responsible for Lorentz contraction or time dilation. The coordinate change is.

Again, where did you get these ideas from? I'm genuinely interested.

I am too; TCS you've expressed what I would charitably call a constellation of weird notions in several threads, and I wouldn't mind knowing where this is coming from. If you are making what feel like natural inferences from limited knowledge, you can be helped. If you're quietly inserting some personal dogma then just let us know so we be done with this.

If there is material out there which is so skewed, it needs to be refuted, and if it has mislead you so badly, starting from the source material is the best way to start that journey.

 

[TCS]

It's the same curvature but viewed in a different frame. The curvature is not responsible for Lorentz contraction or time dilation. The coordinate change is.

Again, where did you get these ideas from? I'm genuinely interested.

http://www.tesisenxarxa.net/TESIS_UIB/AVAILABLE/TDX-0923109-130054//tdda1de1.pdf

The curvature of space time is determined by the stress energy tensor, where the curvature has a vector component, a scalar component and a corection component for the non-commutivity of vectors in the space. When you accelerate, you change the scalar curvature.

 

[nismaratwork]

You're getting this from a doctoral thesis, that from a brief look, does NOT agree with the points you're making? I'm at a loss.

 

[TCS]

You're getting this from a doctoral thesis, that from a brief look, does NOT agree with the points you're making? I'm at a loss.

If you are moving at near the speed of light with respect to the moon, is it not traveling at you with a veloicty near the speed of light?

Does it's mass not increase?

If it's mass increases, does it not warp space time?

None of those notions seem too crazy and that is essentially alll I said in this thread. You can think of it as looking at the universe from a different perspective, but from that perspective the universe has a different basic curvature.

Talking about Einsteins's equations with "flat" uncurved space time seems crazier than anything I have said. Even if the manifold is flat, the space in the manifold is strethced into curves.

The comment about far away objects was off the cuff, but if the trace of the scalar curvature is constant then I think some other part of the universe has to expand.

 

[nismaratwork]

If you are moving at near the speed of light with respect to the moon, is it not traveling at you with a veloicty near the speed of light?

Does it's mass not increase?

If it's mass increases, does it not warp space time?

None of those notions seem too crazy and that is essentially alll I said in this thread. You can think of it as looking at the universe from a different perspective, but from that perspective the universe has a different basic curvature.

Talking about Einsteins's equations with "flat" uncurved space time seems crazier than anything I have said. Even if the manifold is flat, the space in the manifold is strethced into curves.

The problem again, is that you're ignoring coordinate systems.

 

[TCS]

The problem again, is that you're ignoring coordinate systems.

In any coordinate system that you choose, every object will have velocity with respect to every other object. In my coordinate system, the moon is going near C and in the moons coordinate systerm, I am going near C. From my perspective the curvature of the universe looks like one shape and from the perspective of the moon the curvature of the universe looks like another shape. If I acclerate from the Earth to the moon and achieve a speed near C, the shape the moon sees and the shape I see will diverge from each other. From my perspective that change in shape is a warping of space.

 

[Dale]

Does it's mass not increase?

If it's mass increases, does it not warp space time?

This is unfortunately a very common misunderstanding. A fast moving object essentially has no more gravity than a slow moving object of the same rest mass.

Remember, the source of gravity in GR is not just mass, but the entire stress-energy tensor. Yes, as the speed increases the energy term increases, but so do the momentum terms. The net effect is that there is little or no change depending on exactly what you are looking at. Certainly curvature is covariant so you do not go from a flat spacetime to a significantly curved spacetime simply by boosting a small rest mass to relativistic speeds.

 

[Ich]

The curvature of space time is determined by the stress energy tensor, where the curvature has a vector component, a scalar component and a corection component for the non-commutivity of vectors in the space. When you accelerate, you change the scalar curvature.

And I'm supposed to find such notions in Sra. Alic's thesis?

If it's mass increases, does it not warp space time?

If it does, it does so even if it's not moving. But as I said, this has nothing to do with Lorentz contraction od time dilation. Do you claim that it responsible for these effects?

Talking about Einsteins's equations with "flat" uncurved space time seems crazier than anything I have said.

I don't think we're talking about the Einstein Field Equations in this thread.

The comment about far away objects was off the cuff, but if the trace of the scalar curvature is constant then I think some other part of the universe has to expand.

Off the cuff or over your head? I can't even guess what you're talking about here. Trace of scalar curvature?

 

[TCS]

And I'm supposed to find such notions in Sra. Alic's thesis?

If it does, it does so even if it's not moving. But as I said, this has nothing to do with Lorentz contraction od time dilation. Do you claim that it responsible for these effects?

Special relativity holds in your reference frame, in my reference frame, and in all other inertial frames, but if I am accelerating I'm not in an inertial reference frame. When you are changing momentum, I believe that you need to consider general relativity.

I could be mistaken, but it seems like changes in other objects momentum should manifest as changes to the Riemann tensor and changes in your own momentum should manifest as changes to the Ricci tensor and that both will cause changes to the metric.

 

[Dale]

if I am accelerating I'm not in an inertial reference frame. When you are changing momentum, I believe that you need to consider general relativity.

This is another unfortunate and common misconception. You are never "in" or "out" of a reference frame. Your coordinates in different frames will be different, but you will still have coordinates in all reference frames. Accelerated motion can be analyzed just fine in SR, particularly from an inertial reference frame. Generally, as long as your spacetime is flat it is still considered SR even if your coordinate system is curved or non-inertial.

 

[TCS]

This is another unfortunate and common misconception. You are never "in" or "out" of a reference frame. Your coordinates in different frames will be different, but you will still have coordinates in all reference frames. Accelerated motion can be analyzed just fine in SR, particularly from an inertial reference frame. Generally, as long as your spacetime is flat it is still considered SR even if your coordinate system is curved or non-inertial.

Ok, although I still don't quite see how space can be flat. I'm not aware of anywhere in the universe where there is no gravity.

Also, I've never heard of a membrane or a fluid surface that won't deform if a force is applied. The stress energy tensor is just a genralization of an ordinary stress tensor. How can you change the pressure on the space time manifold and not move it?

It would take a lot of energy to make you (a macroscopic object) go 99.999% the speed of light. Why won't you warp space time? I guess that there are some relationships that I don't fully understand. I'm going to try and work towards writing a numerical solution to some simple relativistic systems which will hopefully help me to get a firmer grasp on the physical meaning of some of these concepts. Although, it's been a while since I did any real serious numerical analysis, so it will take me a while.

Anyway, I'll avoid making any more comments until I get a firmer grasp on it all.

 

[nismaratwork]

Ok, although I still don't quite see how space can be flat. I'm not aware of anywhere in the universe where there is no gravity.

Also, I've never heard of a membrane or a fluid surface that won't deform if a force is applied. The stress energy tensor is just a genralization of an ordinary stress tensor. How can you change the pressure on the space time manifold and not move it?

Flat does not mean sans gravity... especially when considering large scales. I think you've been mislead in your visualization of how the SET translated into physical reality. Remember time.

 

[Dale]

It would take a lot of energy to make you (a macroscopic object) go 99.999% the speed of light. Why won't you warp space time?

I already explained this above in my first post about common misunderstandings of GR. Again, the energy is only one component of 10 and for a relativistic particle it is not the only important component.

 

[TCS]

I already explained this above in my first post about common misunderstandings of GR. Again, the energy is only one component of 10 and for a relativistic particle it is not the only important component.

I still don't see how object's shape can change and time can slow down on clock on the object, but space encompasing the object hasn't warped.

 

[Dale]

I still don't see how object's shape can change and time can slow down on clock on the object, but space encompasing the object hasn't warped.

You may want to watch some of the excellent online video lectures for that. Leonard Susskind does an enjoyable treatment of curvature in his lectures on GR which includes the flatness of Minkowski spacetime.

However, in the meantime it may help to think of parallel geodesics. In flat spacetime parallel geodesics will remain parallel, even if they are Lorentz-contracted. In curved spacetime parallel geodesics may not remain parallel along their length.

 

[TCS]

I am too; TCS you've expressed what I would charitably call a constellation of weird notions in several threads, and I wouldn't mind knowing where this is coming from. If you are making what feel like natural inferences from limited knowledge, you can be helped. If you're quietly inserting some personal dogma then just let us know so we be done with this.

If there is material out there which is so skewed, it needs to be refuted, and if it has mislead you so badly, starting from the source material is the best way to start that journey.

Nismarak,

it took me a few times of getting my head beaten against the wall to realize it, but you were right about me being stuck in my own dogma. I had gotten drawn into this subject because I was working on some stuff related to tracking acoustic waves in 3d anisotropic media for geologic imaging and I kept comming across articles about general relativity because people use similar mathematical methods for solving the differential equations.

Anyway, I noticed an apparent similarity in the mathematics and it made me think that quantum mechanics could be modeled as wave fronts or some type of standing waves propagating through a 4d anisotropic media, which made me imagine the media as being energy denisty whose elastic properties caused the energy to collect. Then I was thinking that if atoms are nested layers of equal energy density but greater volume, you get a sort of inverse square layering of energy density but still discrete steps on a micro level and the gradient of energy density could provde a type of gravity in the same way as a refractive gradually reducing index of refraction wave guide.

So I was expecting that the curvature and energy densisty of General Relativty would match the curvature and energy distribution of the manifold I was imagining, which led me to believe that special relatiity was just a special case of general relativity since I was thinking that all deformation corresponded to spatial contraction which is based upon a sum of all the energy densities of all particles at a particular spot.

However, I can know now see the errors of my ways after getting comments form you guys and getting deeper into the math of how the vectors are represented and measured.