Gravitational Time Dilation and Age of Astronaut

[sangan]

Hello Everyone, I am new to this forum.
I understood from sources that space-time is like a fabric. The massive bodies bend the space around it, hence the gravity. If time is 4rth dimension, so, the space is bent in time due to mass. that pretty much explains stopping of time in black holes as the pit would be so deep that time at the edge is perpendicular which means time at edge and deeper wall is the same.

On the ground we are at lower level of time and assume an astronaut who is at higher level of time. Being at the higher level in time, what I understood is, a wider "now" timeframe. Because in 3d world, as we ascend to the higher and higher level in "height", we will be able to visualize wider and wider area of the plane, Similar way as we ascend to higher and higher level in "time", we should be able to visualize wider area of times. By rising to sufficient height in time, We should be able to visualize an entire day of earth, as "now", Its said also that time moves faster as we ascend higher, That is a day on Earth is like say an hour if we are at sufficient height.

But what I don't understand is, If 1 Earth day is like an hour to a farther astronaut, He should age slower than people on earth, But its said, astronaut would age faster due to gravitational time dilation, Someone please help!..

 

[Simon Bridge]

Welcome to PF;

We like to play down the "rubber sheet" analogy here - it is just an analogy, which means that it is wrong.
The way to understand GR is mathematically.

it's said, astronaut would age faster due to gravitational time dilation,...

Who says that - please provide a reference.

i.e. from wikipedia:

For example, ISS astronauts return from missions having aged slightly less than they would have been if they had remained on Earth, ...​

 

[sangan]

Thank you Simon,

Here is the reference from wikipedia, When comparing Relative Velocity Time dilation and Gravitational Time Dilation:

To simplify, velocity and gravity each slow down time as they increase. Velocity has increased for the astronauts, slowing down their time, whereas gravity has decreased, speeding up time (the astronauts are experiencing less gravity than on Earth)

It is well known that, When moving at speeds comparable to speed of light, time slows down, that is astronaut ages slower.

Gravity slows down time as it increases

If so, people on Earth at lower level in time(higher gravity), should age slower than astronaut at a higher level in time(the fourth dimension), Shouldn't it be other way round?

 

[A.T.]

...the pit would be so deep that time at the edge is perpendicular...

There is no time dimension in that analogy you are thinking about. It shows curvature of space only. Gravitational time dilation can be visualized as shown here in the top picture:

http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html

 

[Nugatory]

But what I don't understand is, If 1 Earth day is like an hour to a farther astronaut, He should age slower than people on earth, But its said, astronaut would age faster due to gravitational time dilation, Someone please help!..

There are two two things going on here, and they're working on opposite directions. Gravitational time dilation causes time to pass (very slightly) slower for the earth-bound observer, just as you say. But there is also a speed-dependent time dilatation that slows the passage of time for the astronaut relative to the earth-bound observer. Which one dominates depends on the particular setup. In the case of the orbiting ISS, the velocity-dependent effect is greater, so the astronauts age less.

You shouldn't take any statement that "X ages more than Y" too literally unless all the details of the setup have been specified.

 

[bcrowell]

Gravity slows down time as it increases

If so, people on Earth at lower level in time(higher gravity), should age slower than astronaut at a higher level in time(the fourth dimension), Shouldn't it be other way round?

Whom are you quoting here? This statement is misleading as written, without context.

Gravitational time dilation depends on the gravitational potential, not the gravitational field. The gravitational potential is lower on the earth, higher for the astronaut. Therefore it would tend to make time pass more slowly on the earth.

 

[sangan]

Whom are you quoting here? This statement is misleading as written, without context.

I am quoting from wikipedia.

But there is also a speed-dependent time dilatation that slows the passage..

speed-dependent time dilation is not in point of focus here, because, first I want to understand gravity and time dilation associated with it. Is this image showing bending of space wrong?

If it is right, which direction in time is the space bent near earth?

 

[Simon Bridge]

The quoted section refers to two effect - gravitational and special relativity time dilation.
Heavier clocks are slow, moving clocks are slow.
Astronoughts are lighter but also going very fast.

 

[sangan]

I think I understand it now, If the bending of space in time is depicted as shown in the picture attached, everything falls in place.

Ideally at gravity close to zero, the "now" time-slice is so infinitely less that, even a second on Earth would be like months at that point, Hence astronaut would age faster at that point in space. Even in space beyond earth, gravity of sun, gravity of our galaxy applies, So the near zero gravity would be probably way beyond our galaxy.

And at black holes, where gravity is at very very high levels, events of thousands of years(or millions-doesn't matter) would fall under "now" time-slice. Please correct if I am wrong.

 

[A.T.]

Is this image showing bending of space wrong?

Not wrong, but not relevant to gravitational time dilation (and most of gravitational attraction). It is the geometry of space not spacetime. There is no time dimension in this diagram.

If it is right, which direction in time is the space bent near earth?

The up-down direction in those pictures is not time, so your sketch above is wrong. You misunderstand what intrinsic curvature means. It is not bending in any direction (that would be extrinsic curvature), just a distortion of distances within the shown surface. The up-down direction in that picture has no physical correspondence, it is just needed to show the distortion of distances within the surface. That's why it doesn't matter if the dent goes up or down, because the distances within the surface stay the same if you mirror it up:

http://www.physics.ucla.edu/demoweb/demomanual/modern_physics/principal_of_equivalence_and_general_relativity/curved_space1.gif

If you want to visualize gravitational time dilation and gravitational attraction, the time dimension must be one of the dimensions of the surface:

http://www.physics.ucla.edu/demoweb/demomanual/modern_physics/principal_of_equivalence_and_general_relativity/curved_time.gif

https://www.youtube.com/watch?v=DdC0QN6f3G4

 

[sangan]

Thank you A.T, I will go through the references you have provided and try to get a deeper understanding.

 

[A.T.]

Thank you A.T, I will go through the references you have provided and try to get a deeper understanding.

These might also be useful:
http://www.relativitet.se/spacetime1.html
http://www.adamtoons.de/physics/gravitation.swf
http://www.relativitet.se/Webtheses/tes.pdf

 

[sangan]

Thank you A.T.

There is no time dimension in this diagram.

Technically it is not correct to say, there is no time in that image, It is the two dimensional representation of space and time(hence called spacetime fabric), rather than just space in time as I had thought earlier. Circular lines in the image is time and longer lines perpendicular to it is space. If you take single rectangular portion of that space-time fabric, It is exactly space & time dimensions shown in image below.

https://www.physicsforums.com/attachment.php?attachmentid=71344&d=1405411932

it doesn't matter if the dent goes up or down,

True, In the above 2d fabric of spacetime, it doesn't matter if area near space is shown as dent or bulge. The time near Earth is stretched and space is bent.

space is bent in time due to gravity

Though picture i had shared earlier is wrong, My statement that space is bent in time near Earth still holds good, because considering above picture of space time fabric, space is indeed bent in time.

 

[sangan]

, It is exactly space & time dimensions shown in image below.

Sorry, please find the image below.

 

[A.T.]

Circular lines in the image is time and longer lines perpendicular to it is space.

No. They are both just space coordinates.

True, In the above 2d fabric of spacetime,

There is not time in that 2D fabric. It shows just the spatial geometry. See also:
http://en.wikipedia.org/wiki/Schwarzschild_metric#Flamm.27s_paraboloid

It is exactly space & time dimensions shown in image below.

No. That is a different diagram, showing different dimensions. It is not a part of the above diagram.

space is indeed bent in time.

No, it isn't. Intrinsic curvature is not "bending into something". In the embedding diagram on top of this post the 2D surface representing space has also extrinsic curvature into the embedding 3D space of the illustration. But that embedding space doesn't have a physical correspondence. It is just there for visualization. It is not time.

 

[sangan]

..the 2D surface representing space has also extrinsic curvature into the embedding 3D space of the illustration. But that embedding space doesn't have a physical correspondence.

Could you please elaborate?, For a one dimensional line to be curved, it has to be on a two dimensional plane, for a 2d place to be curved it has to be in a 3d volume, So if we say a 3d space is curved it has to be in a higher dimension right?, If not, in which dimension is it curved?

 

[A.T.]

So if we say a 3d space is curved it has to be in a higher dimension right?

No, that's not what we mean. That would be extrinsic curvature, which in the case of space-time has no physical relevance in GR.

GR is about intrinsic geometry, which can be full described by the distances within the manifold, without referring to any higher dimensional embedding manifolds.

See also: http://en.wikipedia.org/wiki/Curvature

There is a key distinction between extrinsic curvature, which is defined for objects embedded in another space (usually a Euclidean space) in a way that relates to the radius of curvature of circles that touch the object, and intrinsic curvature, which is defined at each point in a Riemannian manifold.