1. In another thread Markus has shown me this visualisation for a particle that is "released" at varying initial velocities and distances from the centre of a variably massive spherical object which is 1 light year in radius .

It is not a black hole so far as I can deduce as its mass can only be varied between zero and .75 of the mass required for an actual black hole.
That is the preamble but my question is hopefully obvious to those of you with an education in topology which I lack.

It explains in the help section (of this graphic) that ,and I quote .

"This view shows the curved 2D spacetime embedded in 3D in a way that preserves distances (the metric).The flat 2d spacetime is rolled together into a cylinder.
Mass creates a bulge by "stretching" the dimensions.

It is the bit I have underlined in bold that I cannot understand even though I am able to rotate the cylinder and count the lines of the grid -I set the mass of the object to either zero or non zero to see the change.

I am not trying to understand (at this point) the theory behind the time dilation.I just want to understand how the actual graphic has been made.

What is the metric that is being preserved?

Is it the overall lenth of the world line of the particle ? Or is it the ratio of (1d) space to Time.

It "looks" to me as if someone has placed a hand at either end of the cylinder and squeezed and clearly the program has done something like that but there seems to be a constraint in one or more the other parameters that I just can't puzzle out yet.

Alternatively is this just meant to be a rough representation that will only become clear once I have a bit more of the theory under my belt (and assimilated)?

2.

3. Originally Posted by geordief
What is the metric that is being preserved?
What is meant by this is simply that spatial distances in this animation are taken to remain the same ( bottom left diagram doesn't change at all ); the bulge appears because in the presence of mass, coordinate time becomes "stretched" as seen from the moving observer, i.e. it takes longer coordinate time to travel the same distance. In other words - the time coordinate ( red grid lines ) becomes "stretched out" due to the presence of mass, whereas the spatial part ( the dark blue gridlines ) remain equally spaced everywhere.

It should be noted also that the proper time of the travelling particle is taken as the reference point ( which is why that purple circle at the bottom of the cylinder never changes ), and the turquoise line is a far away clock as seen from the point of view of the travelling observer. What is plotted is the relation between the two.

Alternatively is this just meant to be a rough representation that will only become clear once I have a bit more of the theory under my belt (and assimilated)?
No, this is actually a very accurate simulation - the numbers are all exact. So far as gravitational time dilation is concerned, this is probably as close as you can get to a "real" visualisation.

4. thanks again

I am not trying to be obtuse but when I set the mass to zero both the proper time and also the coordinate time come to 25.13 seconds (with an initial velocity of zero ) but if I count the the vertical gridlines there are about 80 -which doesn't seem to correspond to either proper time or coordinate time .

So are those time gridlines (in the top left graphic ) more representative than accurate?

I can " see" that to be "accurate" it might need to choose between reference frames .Is it deliberately "innacurate" so as to choose neither?

Oh and also in the main (right hand side) graphic could the purple ,proper time circle be shown to move by having the arrow move around the circle to "shadow or follow" the object so as to be "level" on the "time " grid? (as it seems to be doing on the top left ,flattened graphic.

I won't object if you need to say that my observations are more confused than helpful (to myself or others).Sometimes I find that my progress in understanding things can be more than slow -perhaps I am trying to bite off a little more than I can chew at this stage.

5. Originally Posted by geordief
I am not trying to be obtuse but when I set the mass to zero both the proper time and also the coordinate time come to 25.13 seconds (with an initial velocity of zero ) but if I count the the vertical gridlines there are about 80 -which doesn't seem to correspond to either proper time or coordinate time .
The grid lines themselves are purely representative in this visualisation; the important point is that in the absence of mass there is no time dilation.

Oh and also in the main (right hand side) graphic could the purple ,proper time circle be shown to move by having the arrow move around the circle to "shadow or follow" the object so as to be "level" on the "time " grid?
Sorry, but I don't really understand what you mean by this.

6. Well to put it another way .As I can see that perhaps the purple arrow itself shouldn't be moving as it is really just there to indicate the direction of(proper) time my backup idea was that it could be informative to show the yellow object rotating around the purple circle (like a shadow)

On reflection I can now see that circle is also at fixed point in space (zero) and so my idea falls down....

Sorry to have been confusing.

It helps to know that the grid is just representative .

As an extra question since I have been thinking about it a little more generally would it be correct to say that it took us longer to watch the journey to the moon than it took the astronauts to experience it first hand?

If they had taken a cine movie of their holiday from lift off to sea rescue and compared its length to that of a corresponding movie taken from earth (beginning at lift off and ending at the same sea rescue) would the astronauts' movie have been a nanosecond shorter ?(or maybe even more -a few milliseconds?)

What about the spacecraft that collected the dust particles from the comet a while back ? That would have been an even greater difference in clocks surely?

7. Originally Posted by geordief
would the astronauts' movie have been a nanosecond shorter ?
That is difficult to answer, since that depends on the astronaut's exact acceleration profile. Generally speaking, the closer one gets to a massive object, the slower one's clock will tick as compared to some very far reference clock, and the same is true for acceleration - the more acceleration one experiences, the less proper time one accumulates. How the numbers pan out in the end depends on the exact details.

8. I think I have noticed from that simulation that time dilation is also caused simply by speed(I set the mass of the spherical body to close to zero and the speed of the object to close to c and the clocks were very noticeably different) .

So suppose an object were to leave the Space Station at a speed of 1 foot per second and were to travel unaffected by gravity for a million or a billion years (proper time) and return along the same path to the Space Station at the same velocity(where the Space Station was still waiting) what would be the difference in clock readings then?

I don't know if it is necessary to specify how the object manages to reverse its course half way-I suspect not.

9. Originally Posted by geordief
I think I have noticed from that simulation that time dilation is also caused simply by speed
There are two types of time dilation : relative time dilation, which affects coordinate time, and is the result of relative motion. And gravitational time dilation, which affects proper time, and is the result of space-time curvature. They are physically distinct effects.

So suppose an object were to leave the Space Station at a speed of 1 foot per second and were to travel unaffected by gravity for a million or a billion years (proper time) and return along the same path to the Space Station at the same velocity(where the Space Station was still waiting) what would be the difference in clock readings then?
The difference in clock readings in the end will be a direct function of the acceleration profile of the travelling observer. The reason is that what clocks measure is proper time, which is dilated in the presence of acceleration; hence there will be a difference in the end.

I don't know if it is necessary to specify how the object manages to reverse its course half way-I suspect not.
Yes, it is necessary.

10. thanks a lot.(very interesting)

11. Originally Posted by geordief
thanks a lot.(very interesting)
I agree. Thanks for bringing this to my attention Geordief and for Markus in his detailed explanation. :-))

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