# Gravity and its effect on time

1. Jun 29, 2010

### 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?

2. Jun 29, 2010

### nismaratwork

3. Jun 30, 2010

### TheIsland24

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

4. Jun 30, 2010

### Staff: Mentor

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.

5. Jun 30, 2010

### nismaratwork

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

6. Jun 30, 2010

### TCS

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.

7. Jun 30, 2010

### Ich

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.

8. Jun 30, 2010

### TCS

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.

Last edited: Jun 30, 2010
9. Jun 30, 2010

### Ich

This has (almost) exactly nothing to do with acceleration, and it's not the source of the effects you described.
No.

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

10. Jun 30, 2010

### 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 occured when you accelrated. However, for observers you will be warping space time as you move through it.

11. Jun 30, 2010

### Ich

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.

12. Jun 30, 2010

### nismaratwork

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.

13. Jun 30, 2010

### TCS

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.

14. Jun 30, 2010

### 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.

15. Jun 30, 2010

### TCS

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.

Last edited: Jun 30, 2010
16. Jun 30, 2010

### nismaratwork

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

17. Jun 30, 2010

### TCS

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.

18. Jun 30, 2010

### Staff: Mentor

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.

19. Jun 30, 2010

### Ich

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?
I don't think we're talking about the Einstein Field Equations in this thread.
Off the cuff or over your head? I can't even guess what you're talking about here. Trace of scalar curvature?

20. Jun 30, 2010

### TCS

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.