Why doesn't the space curvature restore the path of a photon?

[Lazarus]

How does the curvature of space cause a photon

to permanently change its path?

 

All of the diagrams of space curving around

a mass seem tp start with a rectangular grid then

pull the grid down around a mass. The line that

dips comes back up to realign with the original line.

 

So why does the light lensing work?

[ACG52]

All of the diagrams of space curving around a mass seem tp start with a rectangular grid then

pull the grid down around a mass. The line that dips comes back up to realign with the original line.

 

The diagram is only an analogy. It is not an actual diagram of what happens to the geodesics.

[ajb]

You can draw the local light cones on the space-time in question, in small enough regions everything looks like Minkowski space-time. The curvature of space-time courses the light cones to "tip over". Light must follow the edges of these light cones.

[Lazarus]

The diagram is only an analogy. It is not an actual diagram of what happens to the geodesics.

 

 

A photon thinks it is following a straight line. If you put a

dip in the line by bending space the photon will still follow

the line. The line slopes down then slopes up so the

photon should do the same.

 

A penny put into one of those relativity cones in science

shows goes down because of gravity. Gravity is replaced

by curvature of space in the current model. If the photon

did the same thing as the penny, photons would be captured

by the mass.

 

If the "analogy" is not correct, what is the real path of the photon?

 

 

[krash661]

A photon thinks it is following a straight line. If you put a

dip in the line by bending space the photon will still follow

the line. The line slopes down then slopes up so the

photon should do the same.

 

A penny put into one of those relativity cones in science

shows goes down because of gravity. Gravity is replaced

by curvature of space in the current model. If the photon

did the same thing as the penny, photons would be captured

by the mass.

 

If the "analogy" is not correct, what is the real path of the photon?

Just so i understand,

is this what you are referring to ?

 

 

[Janus]

How does the curvature of space cause a photon

to permanently change its path?

 

All of the diagrams of space curving around

a mass seem tp start with a rectangular grid then

pull the grid down around a mass. The line that

dips comes back up to realign with the original line.

 

So why does the light lensing work?

The photon follows a geodesic The gridlines do not follow geodesics.

 

To illustrate the difference, consider the lines of latitude on a globe that run East and West. Only the equator is a geodesic ( or great circle). It creates a circle that bisects the globe.

 

Now imagine that you are facing West standing at N45 latitude. You start walking forward in a straight line. You will naturally follow a geodesic. This geodesic will not follow the 45th latitude line

 

Thus in this image the green line something like the path you'll take. Notice that it does not parallel the red circle which would represent a line of latitude.

 

 

The gridlines in the rectangular grid at like line of latitude in this respect, in that the light's path doesn't remain parallel to them in the region of curved space.

[Lazarus]

Krash,

 

That is exactly the grid that I see everywhere.

 

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Janus,

 

Both I and Isaac would be happy to agree with

you that the photon appears to follow a geodesic

because of gravity.

 

The curvature of space is supposed to replace

gravity as the mechanism for determining the path

of a photon.

 

So the photon should follow the grid line, not the geodesic.

If the proton follows the geodesic didn't it get out

of it's place in curved space? Naughty photon.

 

[krash661]

ok,

in

astronomy magazine

january 2013

pg44

" how gravity's grand illusion reveals the universe "

 

talks about exactly what you are asking.

the problem is it's a lot to type.

i'll try to find some kind of link on it.

[Lazarus]

ok,

in

astronomy magazine

january 2013

pg44

" how gravity's grand illusion reveals the universe "

 

talks about exactly what you are asking.

the problem is it's a lot to type.

i'll try to find some kind of link on it.

 

Krash,

 

Some of the Astronomy Magazine articles are

available online but that article doesn't seem to

be.

 

Perhaps you can explain the essence of the

difference in a short summary.

[Janus]

 

Krash,

 

That is exactly the grid that I see everywhere.

 

---------------------------------------------------------------

 

Janus,

 

Both I and Isaac would be happy to agree with

you that the photon appears to follow a geodesic

because of gravity.

 

The curvature of space is supposed to replace

gravity as the mechanism for determining the path

of a photon.

 

So the photon should follow the grid line, not the geodesic.

 

If the proton follows the geodesic didn't it get out

of it's place in curved space? Naughty photon.

 

 

The only geodesics in a gravity field that are closed loops are ones that are inside the event horizon of a black hole. The geodesic on a globe are closed circles but they are just one type of geodesic. I used that example because it is easy to visualise how a geodesic differs from a artificially assigned grid line. Don't try to make more of the example than waht it is meant.

 

The geodesic that light follows in a gravity field that does not cross an event horizon will take the light back out to flat spacetime, but at a different direction than it entered the field at.

[krash661]

ok, give me some time and i'll simplify it.

[Lazarus]

The geodesic that light follows in a gravity field that does not cross an event horizon will take the light back out to flat spacetime, but at a different direction than it entered the field at.

 

Geodesic, parabola or ellipse, close enough for government work.

Whoops. Sorry, some of the very knowledgeable people who post

on this forum are government people.

 

Your comment is the very thing that I have the question about.

 

Why does it come out in a different direction rather than follow a "grid"?

[Spyman]

If you made a depression in a pool table, like in the image krash661 presented in post #5, a billiard ball placed where the "earth" is and rolled towards the "percieved position of star" wouldn't follow the red line or any other grid lines painted on the surface, instead the curved surface would bend the path such as the yellow line shows, towards the "actual position of star".

 

 

The grid lines are only there to help us see the shape of the cavity, they do not represent the course of passing objects through the depression, as Janus points out in his post #6.

 

Two-dimensional analogy of spacetime distortion generated by the mass of an object. Matter changes the geometry of spacetime, this (curved) geometry being interpreted as gravity. White lines do not represent the curvature of space but instead represent the coordinate system imposed on the curved spacetime, which would be rectilinear in a flat spacetime.

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

[Lazarus]

The pool table analogy has a problem. It introduces

a force that is not in the situation that we are discussing,

namely the gravitational force towards the center of the

earth.

 

Einstein and Newton both considered the motion of a

photon to be along what it thought was a straight line

unless affected by an external force. If you put a dent

in the space containing the line, the photon should still

continue along the line and eventually be going in the

same direction that it was originally.

 

What would cause the photon to leave the line?

[ACG52]

Einstein and Newton both considered the motion of a

photon to be along what it thought was a straight line

unless affected by an external force.

No, The motion of the photon is along the geodesic. When the photon follows the geodesic into a gravitational field, the geodesic is curved by the field and so the photon follow what is seen as a curved path. But when leaving the field, there is nothing curving the geodesic back to it's original path.

[Lazarus]

I think everybody is in agreement that the photon

really changes direction as an asteroid does when

it passes the earth.

 

My problem was that I was under the impression

that the curvature of space was the only thing

affecting the path.

 

I looks like the proper picture is that, regarding time

as a forth dimension, space curves into a fifth

dimension and there is a gravity like force parallel to

the axis of the fifth dimension.

 

That means Spyman's pool table analogy is pretty good.

 

[Janus]

 

I think everybody is in agreement that the photon

really changes direction as an asteroid does when

it passes the earth.

 

My problem was that I was under the impression

that the curvature of space was the only thing

affecting the path.

Actually, it is the curvature of Space-time.

I looks like the proper picture is that, regarding time

as a forth dimension, space curves into a fifth

dimension and there is a gravity like force parallel to

the axis of the fifth dimension.

This is where the analogy breaks down. We show it as a two dimensional space curved into a third spatial dimension because that's how we can visualize Non-Euclidean geometry. In reality, there is no extra spatial dimension, it's that the rules of geometry in "curved space-time" are based on different postulates than those in Euclidean geometry (which decribes flat space=time).

 

The thing about geodesics are that they are the shortest path between two points. If you follow the a gridline from the point it enters curved space until it leaves, you will find that it is not the shortest path between those points. the shortest path is a curve that intesects the gridline at these two points, at an angle. Light always follows the shortest path. Light following the gridline in flat space-time will follow the geodesic that is parallel to its path upon entering curved spacetime. That geodesic will lead to a point in flat space-time, from which the light will continue on in flat space-time, in a different direction than it entered as seen from flat-space time.

[Lazarus]

Since Cartesian coordinates and space are

different things, a curved 3 dimensional space

can be represented by 4 Cartesian dimensions.

Throw in time and that makes 5 dimensions. If

space is curved in 3 dimensions it takes 7

Cartesian coordinates.

 

The shortest distance between any 2 points on

a "grid" line may be along the line. Consider a

grid fine enough that a misshapen rectangle is

nearly flat and the grid line around it nearly straight.

 

With 4 adjacent "rectangles" the grid line across

the center is the shortest path between the 2 ends.

Now fold it along the vertical centerline to match the

curvature of the well. The crooked line is still the

shortest distance as long as we stay in our space.

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Fold here

 

The sun should be at the bottom of the well.
I still can't see any reason why the photon

should turn towards the center of the well.

 

The only way it can get closer to the center

of the well is to go deeper into the well. If it

did that it should continue down the well just

like the penny does in the science displays.