Why does an orbiting body slow down in curved space-time?

[shehri]

Hi members,

Can someone tell me the simple analogy of curved time & space.I've searched the google but have not been able to find an A-LEVEL STUDENT stuff.I need an introductory & beginner level idea.Thanks...

 

[Naty1]

Have you seen the bowling ball on a stretched rubber sheet analogy? The deformation is analogous to the curving of spacetime...See Wikipedia for "Spacetime"...there is an illustration...

also try for "geodesics" for understanding how "straight lines" become "curved".

Note the "SEE ALSO" section at the bottom of each of the above references for more...

 

[CaptainQuasar]

One thing that isn't conveyed by the bowling ball on a rubber sheet analogy is that time moves more slowly the deeper you are in a gravity well, in addition to the force of gravity being present.

⚛​

 

[A.T.]

Can someone tell me the simple analogy of curved time & space.

Brief introduction:
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html
Longer introduction:
http://fy.chalmers.se/~rico/Theses/tesx.pdf (chapter 2)
Interactive visualization:
http://www.adamtoons.de/physics/gravitation.swf

 

[Dale]

Much of what you need to understand about curved spacetime can be understood by considering geometry on the surface of a sphere.

 

[Colin Mitch]

One thing that isn't conveyed by the bowling ball on a rubber sheet analogy is that time moves more slowly the deeper you are in a gravity well, in addition to the force of gravity being present.

⚛​

Hello Captain, I am interested in the curved time component of gravity waves. Since time moves more slowly in curved space-time (relative to time in flatter space-time) does this mean that there is a (tiny) time-slowing effect when a gravity wave passes? If so, could this be measured in a gravity wave detector on Earth or would we need a clock well out of the gravity wave to compare our clock with?
I guess the fact that there is only one time dimension would mean that all clocks in the gravity wave would be effected alike whereas with space we can use the different effect on 2 space dimensions to detect a gravity wave in a LIGO.

 

[Naty1]

Colin...try Wikipedia at

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

for a decent discussion of gravitational waves, an illustration, and external links at the bottom.

The article mentions the sun/earth gravitational wave power at 313 watts...so its REALLY weak...I assume time would be affected SLIGHTLY but so far nobdoy has even been able to unambiguously detect a gravitational wave let alone second order effects.

 

[feynmann]

Hello Captain, I am interested in the curved time component of gravity waves. Since time moves more slowly in curved space-time (relative to time in flatter space-time) does this mean that there is a (tiny) time-slowing effect when a gravity wave passes? If so, could this be measured in a gravity wave detector on Earth or would we need a clock well out of the gravity wave to compare our clock with?
I guess the fact that there is only one time dimension would mean that all clocks in the gravity wave would be effected alike whereas with space we can use the different effect on 2 space dimensions to detect a gravity wave in a LIGO.

No, gravity wave does not cause time to slow down, it only cause the space to warp
See Shutz's book, Gravity from the Ground up

 

[altonhare]

Hi members,

Can someone tell me the simple analogy of curved time & space.I've searched the google but have not been able to find an A-LEVEL STUDENT stuff.I need an introductory & beginner level idea.Thanks...

I'll repeat the analogy I've illustrated before.

In the "4D space-time" of GR time is essentially just another "direction" in which an object can move. Supposedly we just can't "see" it because we are "trapped" in a 3D perspective.

So, if we consider a flexible sheet with stick figures drawn on it, and imagine that they can only move on/in the sheet itself, we can see that the inhabitants of "Flatland" have no concept of "up". They can only see directly in front, behind, and to the side of them, but never "up". In this analogy our "dimension" of "time" is similar to the Flatlander's "up".

Now let's say there is a deep depression in the sheet and a Flatlander is down in it. There's another Flatlander outside, in the flat area, watching the trapped one. As the trapped one travels out of the depression s/he is mostly moving "up" instead of across. So, while the trapped Flatlander is making considerable total progress in THREE dimensions, most of it is in the "up" direction which the observer and the trapped cannot perceive. Therefore the observer sees the trapped Flatlander moving very slowly (just a little bit "across" but a lot "up").

As the trapped one escapes the depression the sheet becomes less and less vertical and the outside observer sees him accelerating (he moves more "across" and less "up"). The trapped one could have been moving the exact same speed (in 3 dimensions) all along but because the Flatlanders can't see one of them, they are deceived.

This analogy isn't quite there yet, because in addition to simply moving in an unseeable "up" (or time) direction, the surface on which the trapped Flatlander is moving is stretched. If before the surface was flat with a surface area A, and we placed an object (a circle?) somewhere and caused a depression, we now have a total surface area B>A. So the trapped flatlander not only appears to move more slowly because of his/her progression in an unseeable direction, but actually does move more slowly because the sheet itself is stretched out (a "meter" is "further" now than before).

 

[Colin Mitch]

No, gravity wave does not cause time to slow down, it only cause the space to warp
See Shutz's book, Gravity from the Ground up

In that case why is a gravity wave billed as a wave in space-time, not just a wave in space?
Curved space-time slows clocks ie clocks slow in a gravitational field (as compared with clocks out of the gravity field)
That is what makes me think that a gravity wave should slow a clock. Colin

 

[T.O.E Dream]

Hi members,

Can someone tell me the simple analogy of curved time & space.I've searched the google but have not been able to find an A-LEVEL STUDENT stuff.I need an introductory & beginner level idea.Thanks...

An object no matter what, moves through space and time (unless your thinking of parallel universes) because that's the way it is. if it does't i have no idea what it moves through because every thing is space and time. so a very massive object (i'm using a massive object because that's when gravity is really effective) like the sun warps this "fabric" of space and time, (you can think of space and time as a 2D fabric like the sheet on a trampoline). so an example would be a bowling ball on the trampoline and when an object like a tennis ball representing the Earth moves on this fabric it will move on it even if it curves or "warps" (or else it would be in midair). so if the sun curves spacetime, the Earth will move on it because again then it wouldn't be traveling through spacetime. since it's curving from it's center, spacetime will curve in that way. so if we travel through spacetime even if it's curved we will curve toward's the object's center. i know my writing didn't flow so much but if you got the idea that's great.

 

[Dreads]

As i understand it with the rubber sheet bowling ball analogy gravity is due to the curvature of time and not due to a force is that right?

 

[A.T.]

As i understand it with the rubber sheet bowling ball analogy gravity is due to the curvature of time and not due to a force is that right?

Yes, curvature of time is crucial. Unfortunately the rubber sheet bowling ball analogy doesn't show it, as it doesn't contain the time dimension. For better analogies follow the links in this post:
https://www.physicsforums.com/showpost.php?p=2046692&postcount=4

 

[Dreads]

if gravity is due to curved time I take it moving towards a mass does not involve work (ie no energy is expended by either mass) as there is no force involved ?

But if this is the case how come moving away from a mass does involve work?

 

[A.T.]

if gravity is due to curved time I take it moving towards a mass does not involve work (ie no energy is expended by either mass) as there is no force involved ? But if this is the case how come moving away from a mass does involve work?

You need a force to make a mass follow a non geodesic(curved) path in space time. Work is done if the mass moves in space in the direction of that force.

 

[Dreads]

You need a force to make a mass follow a non geodesic(curved) path in space time. Work is done if the mass moves in space in the direction of that force.

Is space and time curved or only time?

If a meteorite is moving in a straight line(ie direct hit) towards the Earth then is it following a geodiesic path? I say it must be as no external force is acting on the merteorite and it is simply following curved time. Therefore do you agree a straight line is a geodiesic path?


Assuming you agree with the above from your logic

if a meteorite (M) moves towards Earth (E) following a geodeisc path, energy expended by E = 0 energy expended by M = 0

if a meteorite (M) moves towards Earth (E) following a striaght line (ie direct hit) as a striaght line is a geodiesic, energy expended by E = 0 energy expended by M = 0

Now if I move a meteorite (M) AWAY from the Earth (E) along a geodeisc path energy expended by E = 0 energy expended by M = 0 energy expended by me = 0

and

if I move a meteorite (M) AWAY from the Earth (E) in a striaght line (ie a line perpendicular to a 2d tangential plane to the surface of the earth), as a striaght line is a geodeisic path, you are saying energy expended by E = 0 energy expended by M = 0 energy expended by me = 0

I disagree

if I move a meteorite (M) or anything for that matter AWAY from the Earth (E) in a striaght line (ie a line perpendicular to a 2d tangential plane to the surface of the earth) then energy will be expended and energy expended by E = 0 energy expended by M = 0 energy expended by me > 0

Further I contend if I move any mass away from any other mass along any path, as long as the nett distnace between the two massess is increasing, then energy will be expended

 

[A.T.]

Is space and time curved or only time?

Both, but space curvature is not so relevant for gravity. http://www.physics.ucla.edu/demoweb/demomanual/modern_physics/principal_of_equivalence_and_general_relativity/curved_spacetime.html"

IIf a meteorite is moving in a straight line(ie direct hit) towards the Earth then is it following a geodiesic path? I say it must be as no external force is acting on the merteorite and it is simply following curved time. Therefore do you agree a straight line is a geodiesic path?

You have two things here:
- The path of the meteorite in space, which is a line
- The path of the meteorite in spacetime, which is a geodesic
For the free fall case they are both geodesics, but not for the lift case:

if I move a meteorite (M) AWAY from the Earth (E) in a striaght line (ie a line perpendicular to a 2d tangential plane to the surface of the earth), as a striaght line is a geodeisic path, you are saying energy expended by E = 0 energy expended by M = 0 energy expended by me = 0

No. If you apply a force to move the meteorite away of the earth, its path in spacetime is not a geodesic, even if the path in space is a geodesic (a line ).

 

[Mentz114]

Hi Dreads,

If a meteorite is moving in a straight line(ie direct hit) towards the Earth then is it following a geodiesic path? I say it must be as no external force is acting on the merteorite and it is simply following curved time. Therefore do you agree a straight line is a geodiesic path?

(my bold)
It's only a geodesic if the meteorite is in free fall. If a rocket ship followed the same spatial route with it's engines running, that would not be a geodesic. Geodesics involve time as well as space.

Further I contend if I move any mass away from any other mass along any path, as long as the nett distnace between the two massess is increasing, then energy will be expended

What about something in a very elliptical orbit which can move away from the capturing mass. In this case kinetic energy is being turned into potential energy as the orbiting body slows down. I don't know where the work is being done.

M

[Edit : I hadn't seen AT's post when I wrote this. ]

 

[Dreads]

What about something in a very elliptical orbit which can move away from the capturing mass. In this case kinetic energy is being turned into potential energy as the orbiting body slows down. I don't know where the work is being done.

Sorry Mentz the quote thing didnt work properly but referring to "orbiting body slows down" Why is the body slowing down? What force is making it decelerate?

 

[Dreads]

so if i fire a gun striaght up is the bullet in freefall as soon as it exits the barrel. ie the force due to the gun powder is no longer acting on the bullet?

 

[Mentz114]

so if i fire a gun striaght up is the bullet in freefall as soon as it exits the barrel. ie the force due to the gun powder is no longer acting on the bullet?

Yes, it's in force free motion.

Sorry Mentz the quote thing didn't work properly but referring to "orbiting body slows down" Why is the body slowing down? What force is making it decelerate?

In Newtonian terms it is 'feeling a force', but in GR terms it is merely following a path where the velocity is constrained to have certain values at certain times. There is 'coordinate acceleration' but that is the kind you can't feel ( ie detect with an instrument).